Wiley: Mathematical Methods in the Applied Sciences: Table of Contents

Hermite Wavelet Operational Matrix Method for Solving Neutral Coupled Delay Differential Equations With Multiple Delays

Saranya Krishnamoorthy, Swaminathan Ganesan, Hossein Jafari — Wed, 10 Jun 2026 05:26:26 -0700

ABSTRACT

Neutral delay differential equations (NDDEs) are established in various applications, such as signal processing, control systems, epidemiology, and dynamical systems. In this research work, we introduce the Hermite wavelet operational matrix (HWOM) method of derivatives to approximate the solutions of NDDEs and systems of pantograph equations. HWOM is a computational algorithm to convert the NDDEs and the system of pantograph equations into an algebraic system with the help of sparse types of matrices. This is demonstrated through several illustrative examples. Furthermore, the obtained HWOM results are compared with exact and other numerical solutions. The efficiency of the proposed method is analyzed through the convergence and error analysis. Satisfactory agreement with the proposed method in terms of improving performance, accuracy, and robustness, and reducing computational cost.

Energy Shaping of Distributed Port‐Hamiltonian Systems Based on Finite Volume Approximation

Fu Zheng, Ziwei Zhang, Sizhe Wang — Wed, 10 Jun 2026 04:56:30 -0700

ABSTRACT

This work introduces a semi-discrete formulation for a class of infinite-dimensional port-Hamiltonian systems (PHS) through a finite volume approach. After spatial discretization, the resulting models maintain the core structural properties of PHS, including the underlying Dirac structure, which is preserved in the absence of external interconnections. A key aspect of this approach involves the integration of a finite-dimensional controller with the infinite-dimensional system through a power-conserving interconnection. Furthermore, we establish a criterion for the existence of discrete analogs of Casimir functions in the discretized framework. The methodology is illustrated through its application to the Timoshenko beam model, where a discrete Casimir function is effectively constructed, reflecting the essential features of the continuous case.

Development of Chelyshkov Wavelets Neural Network Method for Solving Nonlinear Fractal–Fractional Optimal Control Problems

Parisa Rahimkhani, Seydi Battal Gazi Karakoc, Thabet Abdeljawad — Tue, 09 Jun 2026 02:33:30 -0700

ABSTRACT

This paper employs Chelyshkov wavelets neural network method for solving nonlinear fractal–fractional optimal control problems (FFOCPs) in the Atangana–Riemann–Liouville sense. The described neural network is comprised of three layers: the input layer, the hidden layer, and the output layer. This three-layer structure allows the neural network to learn complex relationships between input and output by applying Chelyshkov wavelets in the hidden layer and nonlinear scaling in the output layer. Initially, the problem under investigation is transformed into an equivalent variational problem by applying the definition of the fractal–fractional integral. Subsequently, by utilizing the Chelyshkov wavelets, the neural network method, and the Gauss–Legendre integration, the problem is reformulated as a system of algebraic equations. Finally, this system is solved using Newton's iterative method. Additionally, we show the convergence of the proposed approach within the Hilbert space framework. To assess the applicability and efficacy of the proposed scheme, four examples are given.

New Exploration on Approximate Controllability of Nonlinear Ψ$$ \Psi $$‐Hilfer Fractional Neutral‐Type Delayed Integro‐Differential Stochastic Inclusions

Om Prakash Kumar Sharma, Ramesh Kumar Vats, Ankit Kumar — Mon, 08 Jun 2026 16:56:39 -0700

ABSTRACT

The main objective of this paper is to investigate the sufficient conditions for the existence of mild solution and approximate controllability results for a class of nonlinear fractional neutral-type integro-differential stochastic inclusions with infinite delay in a separable Hilbert space. In the proposed control system, the Ψ$$ \Psi $$-Hilfer fractional derivative has been considered, which has a quality to choose a suitable kernel function Ψ$$ \Psi $$. First, by making use of the Ψ$$ \Psi $$-Riemann–Liouville fractional integral operator, the proposed stochastic control problem is converted into an equivalent fixed point problem, and then, the Bohnenblust–Karlin fixed point theorem is applied to derive the existence of the mild solution. The approximate controllability result for the proposed control system has been established under the consideration that the corresponding linear system is approximate controllable. The theory of multivalued maps, fractional calculus, the concept of stochastic analysis and the fixed point technique have been used to bring off the main results. At the end, we provide a concrete example in order to validate the abstract findings.

Chaotic Dynamics of Hyperbolic Bioheat Models in Banach Space 𝕐σ

El‐mahdi Nafia, Abdellah Taqbibt, M'hamed El Omari — Sun, 07 Jun 2026 23:21:02 -0700

ABSTRACT

This paper investigates the chaotic dynamics of the hyperbolic bioheat equation in the Banach intersection space 𝕐σ=ℍσ∩L2(ℝ+,ℂ). We show that the associated operator 𝔸 generates a strongly continuous C0$$ {C}_0 $$- semigroup on 𝕐σ and establish Devaney chaos by applying the original Bayart-Grivaux eigenvector field criterion. Moreover, we identify invariant spectral subspaces where the semigroup exhibits exponential stability.

Global Stability of a Diffusive Leslie‐Gower Type Model With Intraspecific Competition

Norberto Aníbal Maidana — Sun, 07 Jun 2026 23:00:58 -0700

ABSTRACT

The aim of this work is to improve the global stability results for reaction-diffusion Leslie-Gower type models in a bounded domain Ω∈ℝn$$ \Omega \in {\mathbb{R}}^n $$, with no-flux boundary conditions. Our approach involves constructing a novel Lyapunov function by modifying a previously known one. This approach can also be applied to other reaction-diffusion models.

Robust Dynamic Output Feedback Control for Fractional‐Order Systems

Ying Guo, Chong Lin, Yong Han — Sun, 07 Jun 2026 22:44:00 -0700

ABSTRACT

This article investigates the problem of robust dynamic output feedback control for a class of fractional-order systems with polytopic uncertainties, where the system order satisfies 1≤α<2$$ 1\le \alpha <2 $$. Based on linear matrix inequalities (LMIs), necessary and sufficient conditions for the existence of a dynamic output feedback controller for the nominal fractional-order systems are derived. The proposed approach effectively reduces the conservatism inherent in existing methods, particularly when dealing with polytopic uncertainties. Numerical simulations demonstrate the effectiveness and robustness of the proposed method in stabilizing both nominal and uncertain fractional-order systems.

Invariance Analysis, Optimal System, and Wave Propagation of Solutions of (3+1)‐Dimensional Broer–Kaup–Kupershmidt (BKK) Model in Shallow Water Dynamics

Vikas Dhaka, Astha Chauhan — Sun, 07 Jun 2026 16:41:26 -0700

ABSTRACT

The paper investigates a (3+1)-dimensional (D) system of Broer–Kaup–Kupershmidt (BKK) equations using the method of Lie group analysis to understand the dynamics of nonlinear gravity and long waves in fluid phenomena. Using symbolic computation, we derive infinitesimal generators, vector fields, and the optimal system of the subalgebras. For different cases, we perform the similarity reductions utilizing the optimal system. The similarity reduction reduces the nonlinear partial differential equations (PDEs) into the nonlinear ordinary differential equations (ODEs), which provides closed-form group invariant solutions. As a result, a plethora of exact solutions, including solitary and periodic wave type solutions, are obtained for the considered model. The obtained solutions contain the arbitrary parameters and functions, offering significant potential for modeling shallow water wave propagation and complex geophysical fluid dynamics. To further analyze the results, we plot the obtained closed-form solutions into three-dimension, which shows how the solutions evolve across the varying parameters. All the solutions derived are new and distinct from the earlier findings. We compare our results with the existing solutions presented in the literature highlights similarities, differences, and potential advancements. The figures plotted in this paper demonstrates the variation effects of the nonlinear parameters to the BKK system on the evolution of solitons. The physical structure of the solutions varies significantly with changes in parameters. The physical significance of the obtained solutions is discussed in detail, which demonstrates the model's capacity to describe multidimensional nonlinear wave interactions. The obtained solutions have potential applications in nonlinear physics, quantum mechanics, and optical fibers. The symbolic computations involved in this study were carried out utilizing the software Mathematica and Maple.

On the Controllability of a Class of First Order Impulsive Differential Equations

Wafaa Salih Ramadan, Svetlin G. Georgiev, Waleed Al‐Hayani — Sun, 07 Jun 2026 16:21:20 -0700

ABSTRACT

We provide a new result about the exact controllability of a class of first order impulsive differential equations. To prove our main result we use the Dhage iteration method. The main result is illustrated with an example.

A Computational Study of Radiative Transfer‐Type Equations Involving Fractional Derivatives and Integral Memory Terms

Sabita Bera, Mausumi Sen, Sujit Nath, Bappa Ghosh — Fri, 05 Jun 2026 17:15:04 -0700

ABSTRACT

In this work, we develop and analyze a numerical framework for a time-fractional partial integro-differential equation arising in radiative transfer phenomena. Radiative transfer models are essential for describing the propagation of radiation in complex media, where memory and nonlocal effects often play a significant role. To capture these effects, fractional order formulations have emerged as powerful alternatives to classical models. The existence and uniqueness of the solution are rigorously established, providing a solid theoretical foundation for the model. A stable and accurate numerical scheme is proposed for the considered problem. The scheme employs the L1 approximation on a graded temporal mesh to effectively handle initial time singularities. In addition, a central difference method is used for spatial discretization, while a composite trapezoidal rule is applied to approximate the integral term. Convergence analysis confirms the reliability of the method and provides explicit error bounds. Numerical experiments demonstrate the accuracy, efficiency, and robustness of the proposed approach, highlighting its effectiveness in capturing memory-driven radiative transport processes. Numerical results confirm the physically consistent influence of the scattering coefficient on radiative attenuation. The results indicate that the method is well-suited for practical simulations of fractional radiative transfer problems encountered in physics and engineering applications.

On Variable‐Order Hybrid Caputo–Hadamard Sequential Differential Equations via Darbo Fixed‐Point Theory

Pratibha Verma, Wojciech Sumelka — Thu, 04 Jun 2026 07:11:57 -0700

ABSTRACT

In this paper, we study a boundary value problem for a hybrid variable-order Caputo–Hadamard fractional sequential integro-differential equation with nonseparated boundary conditions. The problem involves variable-order fractional derivatives together with nonlinear integral operators. We reformulate the problem as a fixed point problem in the Banach space of continuous functions. By using the measure of noncompactness and Darbo's fixed point theorem, we prove the existence of solutions. Additional conditions are imposed to obtain uniqueness and Ulam–Hyers–Rassias stability. To support the obtained results, we provide illustrative examples and graphical results. These examples show that the assumptions depend on the choice of the interval [a,1]$$ \left[a,1\right] $$, which in turn affects the admissible region.

Existence of Nontrivial Solutions to a Critical Kirchhoff Equation With a Logarithmic‐Type Perturbation in Dimension Four

Qian Zhang, Yuzhu Han — Wed, 03 Jun 2026 21:40:41 -0700

ABSTRACT

This paper is concerned with the existence of solutions to a critical Kirchhoff equation with a logarithmic-type subcritical term in a bounded domain in ℝ4$$ {\mathbb{R}}^4 $$. Under suitable assumptions on the parameters, we establish the existence of both a positive local minimum solution and a positive ground state solution. Furthermore, by a technical argument, we prove that the local minimum solution is also a ground state solution without additional assumptions. Interestingly, the results show that the introduction of the nonlocal term enlarges the ranges of the parameters such that the problem admits weak solutions, which implies that the nonlocal term has a positive effect on the existence of weak solutions.

On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces

Dušan Oberta — Wed, 03 Jun 2026 21:12:10 -0700

ABSTRACT

In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale. Central role is played by the axiomatic theory of measures of noncompactness and the newly introduced Kamke Δ$$ \Delta $$-function. Also, we study countable systems of dynamic equations on time scales arising from semi-discretization of parabolic partial dynamic equations.

Some Remarks on the Asymptotic Profile of Solutions to Structurally Damped σ$$ \sigma $$‐Evolution Equations

Thi Nga Bui, Tuan Anh Dao, Xiaoyan Li — Tue, 02 Jun 2026 23:16:55 -0700

ABSTRACT

In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for structurally damped σ$$ \sigma $$-evolution equations in L2$$ {L}^2 $$-sense. Depending on the parameters σ$$ \sigma $$ and δ$$ \delta $$ we would like to not only indicate the approximation formula of solutions to both linear and nonlinear problems but also recognize the optimality of their decay rates in the distinct cases of parabolic like damping and σ$$ \sigma $$-evolution like damping when the spatial dimension is sufficiently high. Moreover, some sharp blow-up solution results for the low dimensional cases of the corresponding linear equation are also discussed in this work.

Remarks on the Maximal Regularity for Parabolic Boundary Value Problems With Inhomogeneous Data

Hui Chen, Su Liang, Tai‐Peng Tsai — Mon, 01 Jun 2026 18:40:37 -0700

ABSTRACT

Inspired by Ogawa-Shimizu and Chen-Liang-Tsai on the second and first order derivative estimates of solutions of the heat equation in the upper half space with boundary data in homogeneous Besov spaces, we extend the estimates to any order of derivatives, including fractional derivatives.

Feedback Control Problem for Caputo‐Type Fractional Dynamical System of Higher Order Influenced by fBm With Hurst Parameter

A. Dhanush, V. Vijayakumar — Mon, 01 Jun 2026 16:41:02 -0700

ABSTRACT

In this paper, we address the feedback control problem for fractional differential equations of order 1<δ<2$$ 1<\delta <2 $$, driven by fractional Brownian motion (fBm) with Hurst parameter (HP)12<ℍ<1$$ \left(\mathrm{HP}\right)\kern0.3em \frac{1}{2}<\mathbb{H}<1 $$ in Hilbert spaces. We initially establish the existence of mild solutions through the application of advanced analytical techniques involving fractional calculus, cosine operator theory, stochastic analysis, and Schauder's fixed-point theorem. Under suitable assumptions, we further demonstrate the existence of feasible state-control pairs, which serve as a foundation for constructing optimal feedback control pairs. To validate the theoretical developments, a comprehensive illustrative example is provided, confirming the applicability of the proposed framework.

Carleson Frame Methods for Pantograph‐Type Delay Differential Equations: Theory and Applications

Mutaz Mohammad, Mohyeedden Sweidan, Alexander Trounev — Mon, 01 Jun 2026 16:14:57 -0700

ABSTRACT

We propose a unified analytic-numerical method for pantograph-type delay differential equations based on Carleson frames. The construction exploits the hyperbolic separation of Carleson sequences in the unit disk together with the diagonal action of contraction-induced composition operators on Hardy spaces. Within this setting, solutions are represented through truncated orbits of a bounded operator, leading to redundant but stable frame expansions that naturally reflect the intrinsic self-similarity of proportional-delay dynamics. We establish well-posedness of the discrete scheme, stability of the expansion coefficients, and quasi-optimal convergence, and we further obtain spectral (geometric) convergence for analytic solutions. For a canonical generator, we derive explicit closed-form expressions for the Gram, delay, and derivative matrices, enabling an efficient and numerically robust implementation. Numerical experiments for both linear and nonlinear pantograph equations confirm the theoretical predictions, demonstrating high accuracy, favorable conditioning, and stable behavior under refinement. To the best of our knowledge, this work provides one of the first systematic numerical frameworks for proportional-delay systems based on Carleson frames, and highlights their potential as a mathematically transparent and effective tool for the analysis and computation of such problems.

Wave Dynamics, Stability, and Integrability of a Generalized (3+1)$$ \left(3+1\right) $$‐Dimensional Breaking Soliton Equation

Hitender Kumar — Sun, 31 May 2026 22:10:26 -0700

ABSTRACT

This research investigates the complex behavior of soliton structures governed by the generalized (3+1)$$ \left(3+1\right) $$-dimensional breaking soliton (gBS) equation, a critical framework for modeling nonlinear wave phenomena in fluid dynamics, plasma physics, and optical communications. Despite the importance of these higher-dimensional models in capturing real-world wave breaking and folded patterns, obtaining analytical solutions remains a significant challenge. To address this, we first establish the system's mathematical tractability and integrability through the Painlevé test, confirming its suitability for multi-soliton solutions. A linear stability analysis near the trivial solution (ψ=0)$$ \left(\psi =0\right) $$ is conducted to derive a dispersion relation, revealing that stability regions are governed by an intricate interplay between system parameters and wave vectors. We then employ the generalized Riccati equation mapping method to derive new exact trigonometric, rational, and solitary wave solutions, providing a more diverse set of results than previously reported lump-type or rogue wave studies. Furthermore, phase plane analysis is used to categorize equilibrium points and distinguish between periodic and unstable trajectories. The study's novelty is highlighted by the introduction of a perturbation-based approach that uncovers the transition from stable periodic orbits to quasi-periodic and chaotic dynamics, quantified by the largest Lyapunov exponent. These findings provide essential new insights into the role of nonlinearities in driving system complexity, offering a more comprehensive understanding of wave propagation in higher-dimensional dispersive systems.

Dynamical Behavior of a Heroin Epidemic Model With a Hypothesized Vaccine

Wei Geng, Aikun Teng, Tingting Ma — Sun, 31 May 2026 21:26:14 -0700

ABSTRACT

Heroin abuse has reached epidemic proportions globally. Recent advancements in vaccine development-particularly a novel candidate shown in clinical trials to inhibit heroin-induced euphoria-highlight the potential of immunotherapy as a future cornerstone for addiction treatment. To elucidate the transmission dynamics of heroin use and evaluate the prophylactic impact of vaccination, we formulate an epidemic model incorporating a heroin vaccine. Leveraging methodologies from differential equations and epidemiological modeling, we derive the basic reproduction number R0$$ {R}_0 $$ and rigorously analyze the existence and stability criteria of system equilibria. Notably, the vaccine-free subsystem exhibits backward bifurcation, whereas the heroin-persistent equilibrium attains global asymptotic stability when R0>1$$ {R}_0>1 $$ under specified conditions. Furthermore, numerical simulations underscore the critical role of heroin vaccination in curbing addiction propagation, providing actionable insights for public health strategies.

Exponential Decay for a Wave Equation With a Discrete Time Delay

Waled Al‐Khulaifi — Sat, 30 May 2026 00:35:23 -0700

ABSTRACT

We present a novel approach for treating delay terms broadly, with a specific focus on wave equations. This method allows us to establish exponential energy decay in the presence of a time retardation and the concurrence of a strong damping. Notably, it reveals new types of interactions in which the time delay plays a central role. We show that for small delays, the energy decays exponentially–even when the damping is relatively “weak.” This work introduces a distinct method that adds to our prior contributions as well as the existing treatments of delayed wave equations in the literature.

The Explicit‐Invariant Energy Quadratization Method for the Cahn‐Hilliard‐Navier‐Stokes Phase‐Field Model

Danxia Wang, Jiongzhuo Lv, Bojun Hou — Fri, 29 May 2026 22:20:54 -0700

ABSTRACT

In this paper, we propose an efficient numerical method based on explicit invariant energy quadratization (EIEQ) for the Cahn-Hilliard-Navier-Stokes model. By introducing local and nonlocal auxiliary variables, we linearize the nonlinear terms. Combining the pressure-correction method to handle the velocity-pressure coupling, and using the intermediate velocity (IV) method and the zero-energy-contribution (ZEC) method respectively to solve the coupling between the velocity and the phase-field variable, we construct two fully decoupled, linear, and unconditionally energy stable numerical schemes. Through rigorous theoretical analysis, we prove that both schemes possess unconditional energy stability. Finally, we verify their temporal convergence order and the dissipative property of the discrete energy through numerical experiments. The research results indicate that the proposed methods can efficiently and stably simulate multiphase flow phenomena, providing a reliable numerical tool for complex interfacial dynamics problems.

Anderson Localization for Schrödinger Operator With Denjoy‐Carleman Potentials

Shaojie Chen, Jing Li, Xiaoping Yuan — Fri, 29 May 2026 19:17:19 -0700

ABSTRACT

It is concerned with the Anderson localization for the discrete one-dimensional quasi-periodic Schrödinger operator with some particular Denjoy-Carleman potentials. First, it is proved that when the disorder parameter λ$$ \lambda $$ is sufficiently large and the frequency ω$$ \omega $$ belongs to the strong Diophantine class (with a measure-zero set excluded), the operator satisfies Anderson localization. This demonstrates the exponential localization of eigenstates under these conditions, a hallmark of Anderson localization in disordered systems. Second, for all energy values E$$ E $$, both the Lyapunov exponent and the integrated density of states (IDS) of the Schrödinger operator are shown to be positive. Additionally, these quantities satisfy a specific modulus of continuity, which provides important insights into the regularity and spectral properties of the operator.

Norm and Compactness of a Polynomial Differentiation Composition Operator on the Unit Disc

Stevo Stević — Fri, 29 May 2026 01:09:12 -0700

ABSTRACT

The boundedness of the polynomial differentiation composition operator from the space of Cauchy transforms to the weighted Bergman space on the open unit disk is characterized in terms of the operator symbols and parameters, and some of the quantities and parameters appearing in the definitions of the spaces. Moreover, the norm of the operator is calculated in terms of them. Besides this, some necessary and sufficient conditions for the compactness of the operator are given.

A Refined Delta Laplace Transform Framework for Stability Assessment in Fractional‐Order Dynamical Systems

Yiheng Wei, Xingyu He, Qiang Xu, Jinde Cao — Thu, 28 May 2026 21:37:01 -0700

ABSTRACT

This paper focuses on the stability analysis of delta fractional-order systems with time delays. Several remarkable properties of the delta Laplace transform are exposed and discussed in detail, based on which the stability of delay delta fractional-order systems is investigated systematically. Compared with existing results, this work achieves several key improvements: (i) the fractional-order greater than one is considered for the first time; (ii) the delta Laplace transform is explored and adopted to simplify the stability analysis process; (iii) the area of the stable region is calculated quantitatively and analyzed with visualization methods. Numerical simulations are provided to demonstrate the validity and applicability of the theoretical findings, which also verify that the delta Laplace transform is an essential mathematical tool for analyzing delta fractional-order systems.

A Priori Estimates and Regularity of Solutions to Nonlinear Parabolic Equations in Generalized Morrey Spaces

Tahir S. Gadjiev, Zaur T. Hajiyev — Thu, 28 May 2026 20:59:55 -0700

ABSTRACT

In this paper, we derive generalized Morrey space estimates for the gradient of weak solutions associated with nonlinear parabolic equations in non-smooth domains. Regarding the nonlinearity, we assume it is measurable with respect to the time variable t$$ t $$, while exhibiting small BMO characteristics with respect to the spatial variable x$$ x $$. In addition, we present a numerical application that models the time-dependent propagation of heat or pressure in a subsurface environment using a parabolic PDE and the Crank-Nicolson method, supporting our theoretical findings with visual simulations.

Infinitely Many Solutions for a Nonlocal System Involving Hardy Potentials and Critical Hardy–Sobolev Exponent

Khaled Kefi, Reem Alomair, Mouna Kratou, Kamel Saoudi — Thu, 28 May 2026 06:52:36 -0700

ABSTRACT

In this work, we investigate a specific class of fractional p$$ p $$-Laplacian systems with Hardy potentials and a critical Hardy–Sobolev exponent. By applying the theory of genus combined with variational methods, we establish the existence of infinitely many solutions for the given system.

On Compressible Fluid Flows of Forchheimer‐Type in Rotating Heterogeneous Porous Media

Emine Celik, Luan Hoang, Thinh Kieu — Thu, 28 May 2026 06:42:58 -0700

ABSTRACT

We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of Forchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo-pressure. This parabolic-typed equation can be degenerate and/or singular in the spatial variables, the unknown and its gradient. We establish the Lα$$ {L}^{\alpha } $$-estimate for the solutions, for any positive number α$$ \alpha $$, in terms of the initial and boundary data and the angular speed of rotation. It requires new elliptic and parabolic Sobolev inequalities and trace theorem with multiple weights that are suitable to the nonlinear structure of the equation. The L∞$$ {L}^{\infty } $$-estimate is then obtained without imposing any conditions on the L∞$$ {L}^{\infty } $$-norms of the weights and the initial and boundary data.

Fractional Moment Theory for Anomalous Transport: A Unified Framework for Lévy Flights, Fractals, and Complex Dynamical Systems

Farrukh A. Chishtie — Thu, 28 May 2026 06:27:42 -0700

ABSTRACT

We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power-law behavior. This fractional moment theory addresses the fundamental problem in anomalous transport where traditional integer moments diverge for heavy-tailed distributions characteristic of Lévy flights, continuous time random walks, and chaotic advection. Through rigorous analysis of space-time fractional diffusion equations with Hilfer-composite time derivatives and Riesz-Feller space derivatives, we establish the operator-moment correspondence theorem proving that moments ⟨|x|f⟩$$ \left\langle {\left|x\right|}^f\right\rangle $$ converge if and only if f<α$$ f<\alpha $$, where α$$ \alpha $$ is the Lévy stability index governing asymptotic tail behavior u(x)∼|x|−(1+α)$$ u(x)\sim {\left|x\right|}^{-\left(1+\alpha \right)} $$. We derive from first principles the universal scaling law ⟨|x|f⟩=AfKμ,αf/αtμf/α$$ \left\langle {\left|x\right|}^f\right\rangle ={A}_f{K}_{\mu, \alpha}^{f/\alpha }{t}^{\mu f/\alpha } $$ with explicit coefficient formulas expressed through Gamma functions, establishing connections to Fox H-functions, Mittag-Leffler relaxation, and Wright functions. Complete proofs are provided using multiple independent methods, including self-similarity analysis, Mellin transform techniques, and asymptotic expansions. Applications are developed for turbulent dispersion obeying Richardson's four-thirds law, Lagrangian chaos characterized by finite-scale Lyapunov exponents, anomalous diffusion on fractal substrates, multifractal cascades, relaxation dynamics in glassy systems, epidemic spreading on scale-free networks, and extreme value distributions. The continuous parameter f$$ f $$ enables the extraction of scaling exponents and transport coefficients from systems where variance-based analysis fails entirely.

A Unified Approach to Eberlein Almost Periodic Differential Equations

Z. Zizi, B. Es‐sebbar — Thu, 28 May 2026 06:06:58 -0700

ABSTRACT

We develop a unified approach for proving the existence of Eberlein weakly almost periodic (E.w.a.p.) solutions of differential equations in Banach spaces. The approach avoids the classical requirement of uniqueness of bounded solutions on ℝ$$ \mathbb{R} $$ and relaxes the assumptions usually imposed on the time-dependent coefficients. It applies both to equations with globally Lipschitz nonlinearities and exponentially stable linear parts, and to classes of equations with non-globally Lipschitz nonlinearities. We then illustrate the scope of the main theorem through several applications, including models admitting either unique or multiple E.w.a.p. solutions. In particular, for the logistic equation we prove the existence of bounded solutions on ℝ$$ \mathbb{R} $$ under merely bounded and continuous coefficients. To the best of our knowledge, this extends earlier results, which typically require almost periodic or almost automorphic coefficients. Numerical simulations are included to illustrate the theory.

Equilibrium and Non‐Equilibrium Diffusion Limits for the Compressible Navier–Stokes–Fourier‐P1 Approximation Model of Radiative Flow

Qiangchang Ju, Yongkai Liao — Thu, 28 May 2026 05:11:01 -0700

ABSTRACT

In this paper, we study both equilibrium and non-equilibrium diffusion limits of the compressible Navier–Stokes–Fourier-P1 approximation model arising in radiation hydrodynamics. In the Sobolev functional framework, we establish the uniform estimates of strong solutions with respect to the transport coefficients and prove the convergence to the limiting systems. In the non-equilibrium regime, the limiting system consists of a compressible Navier–Stokes–Fourier system coupled with a diffusion equation, while the radiative equilibrium is achieved between matter and radiation with the leading term of radiation distribution in the equilibrium regime.

Bifurcation and Sensitivity Analyses With Novel Traveling Wave Solutions in a Stochastic Fractional System for Ion Sound and Langmuir Waves

S. Saha Ray — Wed, 27 May 2026 23:13:08 -0700

ABSTRACT

This paper deals with the system of stochastic fractional equations for the ion sound and Langmuir waves. First, the stochastic fractional-order governing system is transformed into a planar dynamical system using a traveling wave transformation. Then, bifurcation analysis is carried out based on planar dynamical system theory, and the sensitivity of the system to perturbation strength and frequency is analyzed. In addition, new traveling wave solutions of the governing system are constructed using two distinct methods: the enhanced Kudryashov method and the improved generalized Riccati equation mapping method. These solutions are essential for understanding various complex and intriguing physical phenomena. Finally, the analysis indicates that fractional-order derivatives and multiplicative noise have a significant impact on the behavior of solutions to the stochastic fractional equations governing ion sound and Langmuir waves.

Correction to Blow‐Up Problem for Porous Medium Equation With Absorption Under Nonlinear Nonlocal Boundary Condition

Alexander Gladkov — Mon, 25 May 2026 22:51:21 -0700

ABSTRACT

Correction to the paper: Alexander Gladkov. Blow-up problem for porous medium equation with absorption under nonlinear nonlocal boundary condition.

Rigorous Analysis of A Nonlocal Transport–Renewal System for Physiologically Structured Populations

Jiguang Yu, Louis Shuo Wang, Ye Liang — Mon, 25 May 2026 22:35:57 -0700

ABSTRACT

We develop a rigorous analytical framework for a class of physiologically structured population models with two internal state variables, nonlocal ecological feedbacks, dynamic resources, inter-zone transfer, and selective harvesting. The full model is a coupled nonlinear PDE–ODE transport–renewal system with endogenous inflow at the recruitment boundary, a setting in which transport, nonlocal dependence, and boundary renewal interact at the same level. For this full nonautonomous multi-zone system, we prove finite-horizon well-posedness in a positive L1$$ {L}^1 $$-based state space, including global existence on arbitrary bounded time intervals, uniqueness, nonnegativity, and continuous dependence on initial data, environmental forcing, and harvesting effort. We then isolate an autonomous single-zone reduction at extinction and construct a positive compact next-generation operator on the recruit space. In a further nonlinear stationary reduction, we prove that supercriticality of the basic reproduction number ℛ0>1$$ {\mathcal{R}}_0>1 $$ yields existence of a nontrivial stationary state under a parametrized compact-operator hypothesis encoding density-dependent renewal feedback. Finally, for a finite-horizon harvest objective over a compact Lipschitz-regular admissible class, we establish existence of an optimal control. The results separate what can be proved for the full climate-explicit system from what can be justified only after autonomous reduction, thereby clarifying the mathematical scope of threshold and control theory for structured populations.

Incorporating Deep Neural Networks with LMI Constraints for Nonlinear Model Predictive Control Optimization

Sayed Allamah Iqbal, Md. Golam Hafez, Asaduzzaman — Mon, 25 May 2026 22:31:22 -0700

ABSTRACT

This paper introduces a deep learning-enhanced nonlinear model predictive control (MPC) framework, in which the control optimization problem is formulated as the minimization of a cost function subject to linear matrix inequality (LMI) constraints. The resulting constrained optimization is solved via semidefinite programming (SDP), ensuring feasible control inputs with robust stability and performance guarantees. To extend stability analysis beyond local linear approximations, deep neural networks (DNNs) are employed to construct neural Lyapunov functions for nonlinear systems. The framework features a learner-falsifier loop: a learner proposes candidate control policies and Lyapunov functions, while a falsifier systematically searches for counterexamples that violate stability conditions. This iterative process integrates classical Lyapunov stability theory with deep learning, enabling the optimization of non-convex cost functions and providing an efficient, automated approach to Lyapunov-based control design. The method ensures stability of nonlinear systems under disturbances. Numerical validation—through phase portraits and time-domain trajectory analysis—demonstrates strong agreement between the DNN-derived Lyapunov functions and the solutions obtained from LMI-based optimization, confirming the robustness and efficacy of the proposed integrated LMI-MPC-DNN methodology.

Stability and Bifurcation of a Time‐Varying Delay Generalist Food Chain Model With Double Fear Effect

Xin‐You Meng, Peng‐Fei Zhou — Mon, 25 May 2026 22:12:00 -0700

ABSTRACT

In this paper, we mainly consider a three-species predator-prey model incorporating fear effect, additional food, time-varying delay, and cannibalistic intermediate predator. First, for the model without time delay, not only the positivity and boundedness of solutions are investigated, but also some conditions for local asymptotic stability of all possible equilibriums and global stability of the positive equilibrium are obtained. Then, some conditions for the existence of a Hopf bifurcation of the model with time delay are explored. Next, the global stability of the positive equilibrium of such a model with time-varying delay is investigated. Furthermore, the multiple time scales method is applied to the delay differential system, and a control strategy based on time delay is obtained. Specifically, a time-varying perturbation is introduced to the delay to suppress oscillation. Finally, the theoretical findings are validated through numerical simulations.

Inhomogeneous Discrete‐Time Asymmetric Exclusion or Zero‐Range Processes and Traffic Models

Marina V. Yashina, Mikhail G. Gorodnichev, Alexander G. Tatashev — Sun, 24 May 2026 22:27:26 -0700

ABSTRACT

Versions of stochastic discrete-time totally asymmetric simple exclusion processes (TASEP) and totally asymmetric simple zero-range processes (TASZPR) are considered. The approach is developed in the frame of microscopic models of vehicular traffic. Known facts of discrete-time queueing network theory are used to obtain theorems regarding TASEP and TASZRP. The following discrete-time processes are studied: A TASEP on a closed lattice such that the probability of a particle transition depends on the index of the particle and the number of vacant sites ahead of the particle; a TASZRP inhomogeneous along a closed lattice; a TASEP on an infinite lattice with a finite number of particles such that the probability of a particle transition depends on the number of vacant sites ahead of the particle; and a TASZRP inhomogeneous along an open boundaries lattice. For the processes under consideration, the stationary state distribution is studied.

Sundman‐Like Transformations and the NRT Nonlinear Schrödinger Equation

P. R. Gordoa, A. Pickering, D. Puertas‐Centeno, E. V. Toranzo — Sun, 24 May 2026 22:15:35 -0700

ABSTRACT

We present a new generalization of the well-known power-type Sundman transformation, involving not only powers of the function but also of its derivative, along with its inverse. Our aim is to explore the use of such transformations in the derivation of solutions of ordinary differential equations and in the study of their properties. We then show their usefulness in the framework of the nonlinear Nobre-Reigo-Monteiro-Tsallis (NRT) nonlinear Schrödinger equation. More precisely, we employ them to analyze a family of ordinary differential equations which includes the Lorentzian solutions of the NRT-nonlinear Schrödinger equation for a constant potential. Moreover, an explicit expression for the Lorentzian solitary wave solutions is given, for any real value of the nonlinearity parameter q$$ q $$, in terms of a transformation depending on q$$ q $$ applied to the classical Lorentzian solution with q=1$$ q=1 $$, that is, we succeed in encapsulating the whole nonlinear behavior in the new transformations. In addition, the composition of this transformation with its inverse (with different parameters) allows us to perform a shift in the nonlinearity parameter q$$ q $$. Moreover, a certain subfamily of our generalized transformations, which performs a shift on the nonlinearity parameter q$$ q $$ of the Lorentzian solutions, is found to have a group structure. The same subfamily of transformations allows us, again, to perform a shift in the nonlinearity parameter q$$ q $$, but in this case in the traveling wave solution for a free particle.

On the Fractional Relaxation Equation With Scarpi Derivative

Matija Adam Horvat, Nikola Sarajlija — Thu, 21 May 2026 23:48:04 -0700

ABSTRACT

In this article, we solve the Cauchy problem for the relaxation equation posed in a framework of variable order fractional calculus. After introducing some general mathematical theory, we establish concepts of Scarpi derivative and transition functions, which represent the essentials of our problem. Next, we provide an integral representation for the solution of our initial value problem, where the transition function is chosen arbitrarily. After that, we find an integral representation in several special cases in which we choose the transition function concretely. Finally, we give some numerical insights that prove our theoretical results.

Solutions of Singular Integral Equations Arising From Frictional Sliding Contact of Layer and Stamp Models Using Sinc‐Collocation Methods

Yaser Rostami, Seyed‐Mohsen Ghoreishi, Khosrow Maleknejad — Thu, 21 May 2026 05:24:55 -0700

ABSTRACT

In this article, two approximate methods for solving singular integral equations of the second type with the Cauchy kernel are presented using numerical methods, which is a mathematical model for many practical problems. This objective is based on a process of functions of the Sinc-collocation methods. Using the Sinc approximation with single-exponential and double-exponential transformations, methods are developed. The approximation resulting from these methods transforms the problem into a system of algebraic equations. We have also determined the analysis of the error bounds of the proposed schemes. Finally, the test examples supported by graphs clearly show the reliability and computational efficiency of the proposed schemes.

T(w)o Patch or Not T(w)o Patch: A Novel Biocontrol Model

Urvashi Verma, Aniket Banerjee, Rana D. Parshad — Wed, 20 May 2026 06:33:02 -0700

ABSTRACT

A number of top-down biocontrol models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest-dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest-dependent monotone functional response is introduced into a “patch” such as a prairie strip with AF, and then disperses or drifts into a neighboring “patch” such as a crop field, to target a pest. We show that the pest extinction state is attainable in the crop field and can be globally attracting. The AF model with a patch structure can eliminate predator explosion present therein and can keep pest densities lower than the classical top-down biocontrol model. We provide the first proof of the global stability of the interior equilibrium for the classical AF model. We also observe “patch-specific chaos” – the pest occupying the crop field can oscillate chaotically, while the pest in the prairie strip oscillates periodically. We discuss these results in light of biocontrol strategies that utilize state-of-the-art farming practices such as prairie strips and drift and dispersal pressures driven by climate change.

Human–Wildlife Interactions in a Tropical Forest Context: Modeling, Analysis, and Simulations

Yves Dumont, Marc Hétier, Valaire Yatat‐Djeumen — Wed, 20 May 2026 00:58:55 -0700

ABSTRACT

Anthropisation and excessive hunting in tropical forests threaten biodiversity, ecosystem maintenance, and human food security. In this article, we focus on the issue of coexistence between humans and wildlife in an anthropised environment. Assuming that humans move daily between their residential area and the surrounding forest to hunt, we study a resource-consumer model with consumer migration. A comprehensive analysis of the system is carried out using classical theory and monotone systems theory. We show that the possibilities for long-term coexistence between human populations and wildlife populations are determined by hunting rate thresholds. Depending on the level of anthropisation and the hunting rate, the system may converge towards a limit cycle or a co-existence equilibrium. However, the conditions for coexistence become more difficult as anthropisation increases. Numerical simulations are provided to illustrate the theoretical results.

Composition of Fractional Integral and Derivative Operators: Summarised in Tables

Arran Fernandez — Wed, 20 May 2026 00:19:49 -0700

ABSTRACT

This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption. The principle of analytic continuation for fractional differintegrals, generally underappreciated in the literature, helps to make the results more concise and natural. These results for Riemann–Liouville operators are well known classically, so here are also presented, for the first time, the corresponding results for the general transmuted operators, which include as special cases all fractional differintegrals taken with respect to monotonic functions, of both left-sided and right-sided types. For verifiability and self-containedness, full proofs are included, even for the classical results, as an appendix.

Two‐Dimensional Carreau Law for a Quasi‐Newtonian Fluid Flow Through a Thin Domain With a Slightly Rough Boundary

María Anguiano, Francisco Javier Suárez‐Grau — Tue, 19 May 2026 06:46:45 -0700

ABSTRACT

This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokes flow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a rough boundary of the domain. Employing asymptotic techniques with respect to the domain's thickness, we rigorously derive the effective nonlinear two-dimensional Reynolds model describing the fluid flow. The mathematical analysis is based on deriving the sharp a priori estimates and proving the compactness results of the rescaled functions together with monotonicity arguments. The resulting limit model incorporates contributions of the oscillating boundary and thus, it could prove useful in the applications involving this lubrication regime.

Deep Neural Network Analysis and Optimal Control for a Fractional‐Order Model of HPV and Cervical Cancer

A. El‐Mesady, M. A. Abdelkawy, Muhammad Farhan, Mohammad Izadi — Tue, 19 May 2026 06:17:20 -0700

ABSTRACT

Leveraging the Liouville–Caputo fractional derivative (LCFD), this work constructs a mathematical framework to examine the dynamics of Human Papillomavirus (HPV) transmission and its progression into cervical cancer. We propose a novel fractional-order model (FOM) consisting of five coupled fractional differential equations (FDEs) that represent different population compartments and incorporate essential epidemiological characteristics of HPV infection. To ensure mathematical validity, we rigorously prove that the model's solutions exist, are unique, and remain positive and bounded. Our analysis involves deriving the basic reproduction number R0$$ {R}_0 $$ to establish a threshold for disease persistence, followed by a comprehensive examination of the stability of the disease-free and endemic equilibrium states. Parameter sensitivity analysis identifies key factors influencing disease transmission dynamics. An extension of our framework involves the formulation of a fractional optimal control problem (FOCP), which includes three time-dependent control measures: safe sexual practice promotion (u1$$ {u}_1 $$), vaccination and immunity enhancement (u2$$ {u}_2 $$), and comprehensive cancer screening and treatment implementation (u3$$ {u}_3 $$). By employing Pontryagin's Maximum Principle (PMP), we rigorously derive the set of necessary conditions required for optimal control. To numerically solve and validate the model, a deep neural network (DNN) with Tanh and ReLU activations was implemented within a stochastic framework. The model's fidelity was verified through convergence testing, error distribution analysis, and regression metrics, using the Adams-Bashforth-Moulton (ABM) scheme and with data divided for training (70%), validation (15%), and testing (15%). The proposed methodology yields solutions that align precisely with benchmark data, achieving a best validation performance of 10−10$$ 1{0}^{-10} $$ and a minimum absolute error of 10−12$$ 1{0}^{-12} $$. Numerical simulations of four control strategies demonstrate that while each intervention reduces infection and cancer progression to some extent, the combined strategy proves most effective. This study highlights the pivotal role of the fractional operator in disease dynamics and introduces a novel hybrid approach that integrates deep learning with fractional calculus, offering a computationally efficient and highly accurate tool for analyzing complex epidemiological systems.

Recovering a Time‐Dependent Diffusion Coefficient From Flux Data in a Fractional Diffusion Model With a Higher‐Order Boundary Condition

Bauyrzhan Derbissaly, Medina Kassen, Makhmud Sadybekov, Madi Yergaliyev — Tue, 19 May 2026 02:52:19 -0700

ABSTRACT

We study an inverse problem for a time-fractional diffusion equation with a Robin condition at x=0$$ x=0 $$ and an eigenparameter-dependent higher-order boundary condition at x=1$$ x=1 $$. For the direct problem we prove existence, uniqueness, and regularity of mild solutions. For the inverse recovery of a positive time-varying coefficient k(t)$$ k(t) $$, we introduce a monotone nonlinear operator whose fixed points correspond to data-consistent coefficients. Monotonicity yields uniqueness, and under mild assumptions the associated fixed-point (K$$ K $$-) iteration is monotone, bounded, and convergent. A modal discretization with L1 time stepping implements the iteration efficiently. Numerical experiments corroborate the theory and examine robustness to noise and the effect of the fractional order α$$ \alpha $$.

Issue Information

Mon, 18 May 2026 01:52:58 -0700

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 8625-8631, June 2026.

Global Existence and Blow Up of Potential Well Solutions for a Coupled Wave System With Degenerate Damping and Source Terms

Haiyan Li, Baowei Feng, Donal O'Regan — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we consider coupled nonlinear wave equations with degenerate damping and source terms and prove several results on potential well solutions via careful analysis involving the Nehari manifold. We prove the global existence of the unique weak solution with initial data from the stable part of the potential well. Whereas the solutions blow up in finite time with positive initial energy in the unstable set if the source terms are stronger than both damping terms.

Bounded Solutions for Nonhomogeneous Double Phase Problems With Gradient Dependence

A. Razani, E. Sengelen Sevim — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper investigates the existence of bounded weak solutions to a class of nonhomogeneous double phase problems involving p$$ p $$-Laplacian and q$$ q $$-Laplacian operators with solution-dependent weights. The problem is set on a bounded domain and features a nonlinear right-hand side that depends on both the solution and its gradient. We establish uniform L∞$$ {L}^{\infty } $$ bounds for the solution set through a Moser iteration technique and prove existence results using truncation methods and pseudomonotone operator theory. Our work extends previous results by considering more general weight structures and gradient-dependent nonlinearities under minimal regularity assumptions. The analysis combines Sobolev space theory, variational methods, and careful energy estimates to handle the interplay between the different growth conditions and degeneracies in the problem.

Long‐Time Behavior of Solution to a Chemotaxis System With Singular Sensitivity in Dimension One

Xiangdong Zhao, Tao Pan, Shuangshuang Zhou — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper deals with a chemotaxis system with singular sensitivity ut=uxx+χuvvxx+ru−μuk$$ {u}_t={u}_{xx}+\chi {\left(\frac{u}{v}{v}_x\right)}_x+ ru-\mu {u}^k $$, vt=vxx−v+uv$$ {v}_t={v}_{xx}-v+ uv $$ in a bounded interval Ω⊂ℝ$$ \Omega \subset \mathrm{\mathbb{R}} $$ with χ,r,μ>0$$ \chi, r,\mu >0 $$ and k>1$$ k>1 $$. It is shown that the system possesses a globally bounded classical solution which enjoys the exponential convergence in L∞$$ {L}^{\infty } $$-norm as t→∞$$ t\to \infty $$ depending on the sign of r−μ$$ r-\mu $$.

Existence of Solutions of Semilinear Wave Equations With Time‐Dependent Propagation Speed and Time Derivative Nonlinearity

Kimitoshi Tsutaya, Yuta Wakasugi — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

Consider wave equations with time derivative nonlinearity and time-dependent propagation speed which are generalized versions of the wave equations in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime, the de Sitter spacetime and the anti-de Sitter space time. We show lower bounds of the lifespan of solutions as well as the global existence by providing an integrability condition on the propagation speed function, which is applicable to the nonlinear wave equation in the expanding FLRW spacetime including the de Sitter spacetime. We also prove that blow-up in a finite time occurs for the generalized form of the equation in contracting universes such as the anti-de Sitter spacetime, as well as upper bounds of the lifespan of blow-up solutions.

Saint‐Venant Estimates and Liouville‐Type Theorems for the Stationary MHD Equation in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$

Jing Loong, Guoxu Yang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we investigate a Liouville-type theorem for the MHD equations using Saint-Venant type estimates. We show that (u,B)$$ \left(u,B\right) $$ is a trivial solution if the growth of the Ls$$ {L}^s $$ mean oscillation of the potential functions for both the velocity and magnetic fields are controlled. Our growth assumption is weaker than those previously known for similar results. The key idea is to refine Saint-Venant type estimates by employing an approach analogous to the Frullani integral.

Some Results for Generalized Proportional Fractional Integro‐Differential Equations With Multi‐Point Boundary Conditions

Zaid Laadjal, Rabiaa Aouafi, Djamila Chergui — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this article, we investigate some new results about the existence, uniqueness and different types of Ulam stability of the solutions for a class of integro-differential equations involving Generalized Proportional Fractional (GPF) derivative of Reimann–Liouville-type with m-point boundary conditions utilizing fixed point theorems with the help of the lower regularized incomplete gamma function and the maximum value of the integral of the Green's function. In addition, by using inequality techniques, we establish new Lyapunov-type and Hartman–Wintner-type inequalities for m-point boundary value problems with GPF derivative that generalizes a recently-obtained result. Moreover, a sharper lower bound of eigenvalues for a Sturm–Liouville eigenvalue problem is obtained. In this respect, we improve some previous results for Mittag–Leffler functions. Finally, we apply the obtained results on a Volterra integro-differential equation involving GPF derivative and GPF integral, and then to Mittag–Leffler functions.

Novel Iterative Methods to Show Classical Solutions of the Rotational Two‐Component Camassa–Holm System

Khaled Zennir, Svetlin G. Georgiev, Aissa Boukarou — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

The rotation two-component Camassa–Holm (R2CH) system is an extension of the well-known Camassa–Holm (CH) equation that incorporates both a second component (often a density or depth variable) and Coriolis-type rotational effects (e.g., modeling Earth's rotation in shallow water dynamics). The paper is devoted to the study of the existence of classical solutions for the rotation two-component Camassa-Holm system, which is a generalization of the Camassa-Holm equation. It is known that the nature of integrable equations allows for an extended search for their various exact solutions. Here, we propose and develop a new iterative method together with certain appropriate topological properties to establish one classical solution for the problem (1) and at least two non-negative classical solutions.

Prey and Predator Inhabitants: Analysis and Direction of Hopf Bifurcation for Optimal Control of Disease Transmission in Prey–Predator Population With Numerical Simulations

Sathish Ram Kumar, M. Kothandapani, B. S. N. Murthy, V. Madhusudanan — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this research, we focus on addressing the eco-epidemiological delay induced prey–predator systems to better understand the dynamic properties of delayed destabilization. However, the question of whether delays contribute to stabilizing or destabilizing the system remains a complex one. We introduce a novel delayed prey–predator interaction with a Holling type-II function response model, where the disease spreads among prey and predator populations susceptible to infection, without considering recovery from infection. The model applies to both species, with the assumption that infected prey, which are less moveable due to the disease, are the only prey consumed by predators both susceptible and infected. In light of these observations, we extend the two-prey, two-predator system to include the effects of control costs on prey reproduction and the switching behavior in predation. We explore several aspects of the model, including the positivity of resolutions, presence of multiple steady states, and the stability and bifurcation at these equilibrium points, all while considering a time delay. Our findings indicate that a Hopf bifurcation can arise near the steady points when the bifurcation parameter representing the incubation period crosses certain threshold values. We further discuss the direction and stability of the Hopf bifurcation at the interior equilibrium point. In the prey–predator system, two types of controls are considered. Isolation, which separates susceptible prey and predator from the infection, and the other provides treatment to minimize deaths caused by the disease. A finite-time optimal control problem is established to minimize the terminal infected prey, predator, and control related costs. Using Pontryagin's maximum principle, the Hamiltonian and adjoint system are derived to characterize the optimal controls. This study highlights the impact of delayed responses such as incubation periods and immunity waning on the emergent eco-epidemiological outcomes and identifies an optimal control strategy that reduces both the density of infected prey, predator, and the associated treatment costs. Simulations are shown to validate the accuracy and practical relevance of these theoretical results.

Scale‐Dependent Modeling of Thermoelastic Damping in Rectangular Nanoplates Considering Surface Elasticity and Nonlocal Thermal Effects

Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In micro/nanoresonators, thermoelastic damping (TED) serves as a principal energy dissipation mechanism that critically determines device performance. The mechanical and thermal responses of these small-scale structures cannot be captured by traditional formulations and demand scale-dependent simulations. This research outlines a fresh modeling approach addressing the role of surface effect in TED for rectangular nanoplate resonators subjected to nonlocal dual-phase-lag (NDPL) heat conduction. The analysis initiates by developing the governing equations for displacement and temperature in Kirchhoff plates through the application of the surface elasticity theory (SET) and the NDPL heat transfer model. The frequency-based technique, combined with the derived equations, yields an explicit TED formulation for nanoscale rectangular plates, accounting for the surface effect. The results section, after confirming model accuracy, delivers various numerical evaluations aimed at assessing the impact of scale effects, plate dimensions, boundary types, vibration modes, and material selections. The analysis implies that TED is attenuated under the influence of non-classical parameters introduced by the SET, in contrast to the higher damping levels predicted by classical elasticity.

Self‐Triggered Impulsive Control for Quasi‐Synchronization of Delayed Memristive Neural Networks

Yujie Liu, Biwen Li — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper investigated the quasi-synchronization (QS) problem of delayed memristive neural networks (DMNNs) by using a self-triggered impulsive control (STIC) strategy. Based on the Razumikhin-type comparison approach for impulsive systems, this study derived the expression of the QS error bound and established several sufficient conditions for achieving QS. Additionally, it was proved that there was no Zeno behavior at the impulsive moments. In the STIC mechanism, the timing of the impulses is determined by a self-triggered mechanism (STM). Compared with the event-triggered impulsive control (ETIC) strategy, the STIC strategy predicts the next impulse instant by using the information from the last impulse instant and the system states, thereby eliminating the need for continuous monitoring of the system states required in the ETIC mechanism. This approach significantly reduces communication costs and the consumption of computational resources. Finally, the effectiveness of the theoretical results is verified through a numerical simulation.

Sampling for Quaternion Bandlimited Signals in the Offset Linear Canonical Transform Domains

Shuli Hou, Yingchun Jiang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

The paper mainly studies the uniform sampling problems of quaternion bandlimited signals in the two-dimensional offset linear canonical transform domains. Based on the systematic analysis for the sampling theory of quaternion bandlimited signals in the Fourier transform domains, we establish the sampling theorems for quaternion bandlimited signals in the offset linear canonical transform domains, where the imaginary units used in defining the transforms are different from those in the quaternion representation. The results show that the sampling formulas have essential differences for the three kinds of transforms, even though the bandlimited rectangular is symmetric about the origin. Moreover, numerical simulations demonstrate the efficiency of the proposed sampling theorems.

Dynamic Analysis of an HBV Infection Model With Capsid, Distributed Delay, and Saturation CTL Immune Response

Chong Chen, Zhijian Ye, Yinggao Zhou — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This study constructs and analyzes an innovative five-dimensional HBV infection model. This model integrates four key biological features for the first time: The role of HBV capsid, two infection routes, namely viruses-cells (VC) and cells-cells (CC) transmission, distributed delay to characterize the time-lag effect in intracellular processes, and cytotoxic T lymphocyte (CTL) immune response with saturated proliferation rate. Two key threshold parameters are established: The basic reproduction number R0$$ {R}_0 $$ and the basic reproduction number of CTL immunity R1$$ {R}_1 $$. The model has three equilibria: The infection-free equilibrium E0$$ {E}_0 $$, the immune-free equilibrium E1$$ {E}_1 $$, and the immune-present equilibrium E2$$ {E}_2 $$. By using the linearization method, Lyapunov function, and LaSalle's invariance principle, the local and global asymptotic stability of each equilibrium is rigorously proven. Our numerical simulation verifies the stability conclusion of the equilibrium. In addition, we not only consider the influence of time delay on the long-term infection of the model, but also consider the influence of the saturation coefficient on HBV. Studies have shown that prolonging the time delay and reducing the saturation coefficient can effectively inhibit viral replication and control the spread of infection. This finding points to a new direction for public health authorities in developing novel drugs: Interventions aimed at prolonging the time delay or reducing saturation are expected to achieve effective disease control.

New Different Envelope and Super Soliton Waves for Physical Kuralay Model Phenomena

Hadil Alhazmi, Sanaa A. Bajri, E. K. El‐Shewy, Mahmoud A. E. Abdelrahman — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This work explored the complicated coupled (1+1)-dimensions Kuralay model, which is an integrable spin mode. The Riccati–Bernoulli subsidiary ordinary-differential equations method has been applied to obtain general mathematical solutions in the form of rational, hyperbolic, trigonometric and exponential solutions. The dynamical properties of this solution forms in our physical model appears in the form of new novel nonlinear solutions as explosive cnoidal solutions, blow up solution, oscillatory, explosive envelope, periodic explosive envelope, stationary explosive, super form, dark and bright envelope solitons. For appropriate free physical parameter values, significant changes in the wave amplitudes of this solutions have been produced without change in phase. The obtained results by proposed method clarify the simplicity and efficacy of our method in examined nonlinear modes used in mathematical physics.

On the Stability of the 2D Boussinesq‐MHD Equations in Two Kinds of Strip Domains

Hao Liu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we investigate the stability of perturbations near the hydrostatic equilibrium of the two-dimensional incompressible Boussinesq-MHD equations with zero resistivity. The absence of vertical dissipation of the magnetic field poses significant challenges to stability analysis. The main technique is utilizing anisotropic estimates and the vertical spatial decomposition, and then we can establish the global stability of a certain stationary (ve,Be,Θe,pe)=0,e1,x2,12x22$$ \left({v}_e,{B}_e,{\Theta}_e,{p}_e\right)=\left(0,{e}_1,{x}_2,\frac{1}{2}{x}_2^2\right) $$ in two kinds of infinite strip domain: ℝ×(0,1)$$ \mathbb{R}\times \left(0,1\right) $$ and ℝ×𝕋.

Boundedness and Asymptotic Stability of Solutions for Fully Parabolic Chemotaxis‐Competition System With Loop and Nonlocal Kinetics

Shuyan Qiu, Li Luo, Xinyu Tu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This article deals with the following fully parabolic chemotaxis-competition system with loop and nonlocal kinetics ut=Δu−χ11∇·(u∇v)−χ12∇·(u∇z)+f1(u,w),x∈Ω,t>0,vt=Δv−v+u+w,x∈Ω,t>0,wt=Δw−χ21∇·(w∇v)−χ22∇·(w∇z)+f2(u,w),x∈Ω,t>0,zt=Δz−z+u+w,x∈Ω,t>0,$$ \left\{\begin{array}{ll}{u}_t=\Delta u-{\chi}_{11}\nabla \cdotp \left(u\nabla v\right)-{\chi}_{12}\nabla \cdotp \left(u\nabla z\right)+{f}_1\left(u,w\right),\kern2.00em & x\in \Omega, \kern1em t>0,\\ {}{v}_t=\Delta v-v+u+w,\kern2.00em & x\in \Omega, \kern1em t>0,\\ {}{w}_t=\Delta w-{\chi}_{21}\nabla \cdotp \left(w\nabla v\right)-{\chi}_{22}\nabla \cdotp \left(w\nabla z\right)+{f}_2\left(u,w\right),\kern2.00em & x\in \Omega, \kern1em t>0,\\ {}{z}_t=\Delta z-z+u+w,\kern2.00em & x\in \Omega, \kern1em t>0,\end{array}\right. $$subject to homogeneous Neumann boundary conditions in an arbitrary smooth bounded domain Ω⊂ℝn(n≥1)$$ \Omega \subset {\mathbb{R}}^n\left(n\ge 1\right) $$, where χij>0(i,j=1,2)$$ {\chi}_{ij}>0\left(i,j=1,2\right) $$, f1(u,w)=u(a0−a1u−a2w−a3∫Ωudx−a4∫Ωwdx)$$ {f}_1\left(u,w\right)=u\left({a}_0-{a}_1u-{a}_2w-{a}_3{\int}_{\Omega} udx-{a}_4{\int}_{\Omega} wdx\right) $$, f2(u,w)=w(b0−b1u−b2w−b3∫Ωudx−b4∫Ωwdx)$$ {f}_2\left(u,w\right)=w\left({b}_0-{b}_1u-{b}_2w-{b}_3{\int}_{\Omega} udx-{b}_4{\int}_{\Omega} wdx\right) $$ with ai,bi>0(i=0,1,2),aj,bj∈ℝ(j=3,4)$$ {a}_i,{b}_i>0\left(i=0,1,2\right),{a}_j,{b}_j\in \mathbb{R}\left(j=3,4\right) $$. Under the appropriate assumption of initial data regularity, it is shown that the corresponding initial-boundary value problem admits a unique global and uniformly bounded solution under some suitable parameter conditions in any spatial dimension. Furthermore, based on some appropriate functionals, the globally asymptotic stabilization of coexistence and semi-coexistence steady states is studied.

The Decay and Extinction of W2,p$$ {W}^{2,p} $$‐Norm and New Blow‐Up Phenomena for a Singular p‐Biharmonic Parabolic Equation With Logarithmic Nonlinearity

QunFei Long — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We in this manuscript restudy the long time decay, extinction and blow-up for a singular p-biharmonic parabolic equation with logarithmic nonlinearity, which appears in many branches of physics. In the framework of potential well theory and the existence of global solution, by a way of establishing a nonlinearly integral inequality without non-increasing condition, we prove that W2,p$$ {W}^{2,p} $$-norm for the weak solutions is non-increasing, and establish two decay and extinction theorems that incorporate two kinds of polynomial decay, two kinds of exponential decay and two kinds of finite time extinction. By a way of establishing an improved Hardy–Sobolev inequality and applying a non-concavity method, we establish the four blow-up theorems independent of the potential well depth with Ju0<M(0)$$ J\left({u}_0\right)<\mathfrak{M}(0) $$ as the blow-up criterion, where two of them are finite time blow-up, one is at least exponential growth and blows up at least at infinity, the last one blows up at infinity, where M(t)$$ \mathfrak{M}(t) $$ is a nonlinear function of ∫ℝn|u(x,t)|2|x|sdx$$ {\int}_{{\mathrm{\mathbb{R}}}^n}\frac{{\left|u\left(x,t\right)\right|}^2}{{\left|x\right|}^s}\mathrm{d}x $$. These generalize previous research results from three aspects: long time decay, extinction and blow-up.

On the Stability of Contact Discontinuity for the 1D Compressible Full Navier‐Stokes‐Allen‐Cahn System With Free Boundary

Dan Lei, Fanfan Jiang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper is concerned with the large-time behavior of solutions to the one-dimensional full compressible Navier-Stokes-Allen-Cahn system with a free boundary. The model can be used to describe the motion of a mixture of two viscous compressible fluids. We first construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation. Then we prove that the viscous contact wave is time-asymptotically stable, provided that the strength of contact wave and the initial perturbation are sufficiently small. The proof is given by the elementary L2$$ {L}^2 $$-energy method.

Wave Structures Influenced by Effective Diffusivity in a Relaxing Gas With Quartic Nonlinearity

Sagar Khairnar, G. Madhumita, V. D. Sharma — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We analyze a quasilinear system of partial differential equations governing the unsteady one-dimensional motion of a relaxing gas with mild dissipation. Using an asymptotic method, we derive a modified Burgers'-type evolution equation that captures simultaneously the effects of relaxation (source term), thermo-viscous dissipation (diffusive term), and nonconvex flux nonlinearity (quadratic–quartic terms), providing a unified evolution model for weak shock structures in relaxing gases. Numerical solutions of the associated Riemann problem reveal some novel phenomena such as sonic and double sonic shocks and Taylor's shock solution.

Inverse Nodal Problem for Singular Sturm–Liouville Operator

Merve Arslantaş, Sevim Durak, Rauf Amirov — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this study, inverse nodal problems are studied for Sturm–Liouville equations with point δ and δ′ interactions. The study proves the existence of a solution to the inverse nodal problem and provides a practical method for finding the solution.

Optimal Control of a Time‐Fractional Model of Cancer with Cell Mutations

Sakine Esmaili — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this investigation, we study an optimal control problem for a parabolic-hyperbolic free boundary problem modeling the growth of a tumor with drug application. In this model, the heterogeneity or different types of tumor cells (caused by mutations and different values of drug and nutrient concentrations inside the tumor) are considered that are included in the model by considering a variable −1≤y≤1$$ -1\le y\le 1 $$. It is assumed that converting from mutation state y1$$ {y}_1 $$ to mutation state y2$$ {y}_2 $$ happens with probability Py1,y2$$ P\left({y}_1,{y}_2\right) $$. This model consists of a first-order hyperbolic equation describing the evolution of tumor cells depending on y$$ y $$. It also includes two time-fractional parabolic equations describing the diffusions of nutrients (e.g., oxygen and glucose) and drug concentrations. In this paper, the concentrations of drug and nutrients on the boundary of the tumor are the control variables, which diffuse inside the tumor and affect the growth of the tumor. A cost function is presented in which the radius of the tumor and the boundary values of drug and nutrients (to limit the side effects of decreasing nutrient and increasing drug) are included. The adjoint equations are presented, and the necessary conditions in terms of adjoint equations are given. The existence and uniqueness of optimal control are also proved. In order to obtain the optimal control values, we have used the direct method. Hence, the problem is discretized using a combination of spectral method and the product trapezoidal approximation for the Caputo fractional order derivative. Then, we have minimized the discretized cost function employing Trust-region reflective algorithm. Taking into account heterogeneity and moving boundary increases the complexity of the model but provides us with a model that satisfies more properties of real tumors. Despite these details added to the model, we have proved the existence and uniqueness of the optimal control. Finally, some figures are also presented to illustrate the effects of optimal controls and noisy controls on the cost functions and radius of the tumor. Noisy controls are obtained by adding noises generated by normal distributions. The cost function and radius of tumor for noisy and optimal boundary values of nutrient and drug are plotted. It is shown the lowest cost function and radius are for optimal controls when the noisy values satisfy the constraints for the control variables considered in the optimal control problem.

Analysis of a Novel Time Filter Algorithm for the Time‐Dependent Incompressible Thermomicropolar Fluid Equations

Fan Wang, YunZhang Zhang, XiaoGang Du, Xinxin Guo — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we present an efficient numerical algorithm for solving time-dependent thermomicropolar fluid equations. The proposed method combines a first-order γ$$ \gamma $$-scheme, based on the linear multi-step method (LM), with a time filter (TF) (referred to as LMTF). This approach enhances the temporal convergence rate from first-order to second-order accuracy while preserving computational efficiency and implementation simplicity. The algorithm first computes the linear velocity and pressure, then solves for the angular velocity, and finally for temperature, effectively decoupling the entire system. We provide a rigorous theoretical analysis of the decoupled LMTF scheme, proving its stability and deriving error estimates. Numerical experiments confirm the algorithm's effectiveness.

Application of Multivariate Bilinear Neural Network Method to a Spatial Symmetric Nonlinear Dispersive Wave Model in (2 + 1)‐Dimensions

Hai‐Peng Wang, Qing Ye, Zhen‐Hui Zhang, Jian‐Guo Liu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this work, the multivariate bilinear neural network method (MBNNM) is applied to derive exact analytical solutions for nonlinear partial differential equations (NPDEs). Specifically, a (2 + 1)-dimensional spatial symmetric nonlinear dispersive wave model (SSDWM) is investigated by integrating MBNNM with established architectures (3-2-2-1, 3-2-3-1, and 3-3-2-1), while a new 3-4-2-1 architecture is developed for further investigation. By systematically selecting generalized activation functions, diverse exact analytical solutions are obtained, with their dynamic behaviors characterized via 3D/2D plots, contour plots, and density maps. To improve the computational efficiency of MBNNM in handling complex equations, a novel matrix-based solution strategy is proposed. This strategy significantly enhances computational performance by transforming the Hirota bilinear expansion into matrices for arithmetic processing.

Exponential Stability of Discrete‐Time Impulsive Stochastic Systems With Delayed Impulses and Markovian Jump

Ting Cai, Yao Cui, Pei Cheng, Mingang Hua — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this work, a new criterion for the exponential stability of p$$ p $$ th moments of discrete-time stochastic systems (DTSSs) with delayed impulses and Markov jump is established based on the Lyapunov method and the Razumikin techniques. The results show that the DTSSs with Markov jump can be exponentially stabilized by the impulse. Moreover, the stability of DTSS with Markov jump without impulses can be maintained with appropriate impulse intervals. Finally, the validity and superiority of the obtained results are demonstrated by some numerical examples.

A Fractional Order Model for the Transmission Dynamics of Meningococcal Meningitis With Real Statistical Data

Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we propose a Caputo-based fractional-order derivative model for the transmission dynamics of meningococcal meningitis (MM), incorporating the environmental concentration of Neisseria meningitidis as well as factors such as vaccination and the hygiene consciousness of susceptible individuals. The existence and uniqueness of solutions to the model are established using Banach's and Schauder's fixed-point theorems. Additionally, we compute the basic reproduction number and examine the local asymptotic stability of the disease-free equilibrium using the Routh–Hurwitz criterion. We analyze the stability of the fractional-order meningitis model using the Ulam–Hyers–Rassias stability method. Furthermore, we fit the model to the cumulative confirmed cases of cerebrospinal meningitis in Nigeria using data obtained from the Nigeria Centre for Disease Control (NCDC) to validate the model. The model demonstrates a good fit with the reported cumulative cases. Numerical simulations are conducted for various values of the fractional order. The results reveal an inverse relationship between the fractional order and the total number of asymptomatic infected individuals (carriers), symptomatic infected individuals, and the environmental concentration of Neisseria meningitidis. This implies that increasing the order of the fractional derivative leads to a decrease in the number of infections and bacterial concentration. Moreover, increasing vaccine uptake and improving hygiene consciousness among susceptible individuals significantly reduce both the number of infections and the environmental concentration of Neisseria meningitidis.

On the Coersive Solution of a Defective Boundary Value Problem

Naila Namazova, Fatma Müslümova, Arzu Safarova, Ahmet Ocak Akdemir — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This study addresses boundary value problems for third-order linear ordinary differential equations with recurring characteristics. By analyzing the principal determinant formed by the boundary conditions, it is shown that the problem is regularly defined with defects within a specific spectral angle; furthermore, the existence of a coercive solution in suitable function spaces for the corresponding non-homogeneous boundary value problem is proven. The results contribute to the theory of boundary value problems with recurring characteristics and offer methods that can be applied to more general classes of such problems.

A Predictor‐Corrector Linearized High‐Order FEM for Nonlinear Time‐Fractional Parabolic Equations With Distributed Delay and Variable Coefficients

Ujwal Warbhe — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper presents a comprehensive numerical framework for solving nonlinear time-fractional parabolic equations with distributed delays and variable coefficients. The proposed method combines the high-order Alikhanov L2$$ L2 $$-1σ$$ {1}_{\sigma } $$ temporal discretization on graded meshes with a novel predictor-corrector quasi-linearization technique for handling the coupled nonlinearity and delay terms. Spatial discretization is achieved through the standard Galerkin finite element method. We establish the unconditional stability of the scheme and derive optimal error estimates of order O(hr+1+Δt2)$$ O\left({h}^{r+1}+\Delta {t}^2\right) $$ in the L2$$ {L}^2 $$-norm and O(hr+Δt2)$$ O\left({h}^r+\Delta {t}^2\right) $$ in the H1$$ {H}^1 $$-norm. Furthermore, we prove a superconvergence result, demonstrating that through appropriate post-processing, one can achieve an enhanced convergence rate of O(hr+1+Δt2)$$ O\left({h}^{r+1}+\Delta {t}^2\right) $$ in the H1$$ {H}^1 $$-norm for sufficiently smooth solutions. The theoretical analysis employs a discrete fractional Grönwall inequality and rigorous error estimates that account for the weak singularity at the initial time. In contrast to existing methods such as Peng et al. (2024), which use first-order L1 temporal discretization, our scheme achieves second-order temporal accuracy and systematically handles variable coefficients and general distributed delay kernels. Numerical experiments validate the theoretical results and demonstrate the method's effectiveness for biologically relevant models, including a fractional Nicholson's blowflies equation with spatial heterogeneity. Additional experiments with higher-order finite elements confirm the higher-order spatial convergence, and condition number analyses demonstrate the mesh-independent performance of the predictor-corrector linearization. The robustness of the algorithm is confirmed through long-time simulations with strongly variable coefficients and distributed delay kernels.

Dynamics of the Critical Choquard Equation With a Focusing Local Perturbation

Jinkai Gao — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we study the following energy-critical Choquard equation with a focusing local perturbation i∂ψ∂t+Δψ+ψq−2ψ+Iα∗|ψ|2α∗ψ2α∗−2ψ=0,t∈ℝ,x∈ℝ3,$$ i\frac{\partial \psi }{\partial t}+\Delta \psi +{\left|\psi \right|}^{q-2}\psi +\left({I}_{\alpha}\ast {\left|\psi \right|}^{2_{\alpha}^{\ast }}\right){\left|\psi \right|}^{2_{\alpha}^{\ast }-2}\psi =0,\kern1em t\in \mathbb{R},\kern0.3em x\in {\mathbb{R}}^3, $$where ψ:ℝ×ℝ3→ℂ$$ \psi :\mathbb{R}\times {\mathbb{R}}^3\to \mathbb{C} $$, q∈2+43,6$$ q\in \left(2+\frac{4}{3},6\right) $$, α∈(0,3)$$ \alpha \in \left(0,3\right) $$, 2α∗:=3+α$$ {2}_{\alpha}^{\ast}:= 3+\alpha $$ and Iα$$ {I}_{\alpha } $$ is the Riesz potential of order α$$ \alpha $$. The existence and qualitative properties of the ground states for this problem have been well studied recently. However, the long-time dynamics of solutions remain unknown. By employing the concentration-compactness and rigidity method introduced by C. E. Kenig and F. Merle (Invent. Math., 166 (2006)), we establish a scattering vs. blow-up dichotomy for radial solutions below the ground state energy threshold.

On Controllability of an Implicit Stochastic Differential Equation With Rosenblatt Process and Non Instantaneous Impulses

Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we examine a class of implicit fractional stochastic differential equations that incorporate non-instantaneous impulses and Poisson jumps, influenced by the Rosenblatt process, which captures long-range dependence and memory effects. The implicit formulation adds significant analytical complexity, requiring the use of sophisticated mathematical tools. To address this, we establish the existence and uniqueness of solutions by employing the fixed-point theorem, in conjunction with the theory of sectorial operators and techniques from stochastic analysis. In addition, we investigate various notions of Ulam's stability, which measure the sensitivity of solutions to initial perturbations and ensure the reliability of the system under small changes. The concept of controllability is also explored, demonstrating that under appropriate conditions, the system can be guided to a desired final state. To illustrate the theoretical results and enhance understanding, two detailed examples are provided, confirming the effectiveness and applicability of the proposed model.

Exponential Stability of Transmission Problem With Distributed Delay and Memory Terms

Jia Liu, Meng Hu, Qiao‐Zhen Ma — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, under appropriate assumptions on the nonlinear weights F(x,t)$$ F\left(x,t\right) $$ and G(x,t)$$ G\left(x,t\right) $$, the balance relationship between damping and distributed delay as well as that between damping and memory terms is investigated. Under such balance conditions, the well-posedness is proved by combining the semigroup approach and the Kato operator perturbation technique. Then, in line with the multiplier method, the exponential stability of the problem is obtained through the construction of an appropriate Lyapunov functional.

A Space‐Time Fourth‐Order Compact Finite Difference Scheme for Semilinear Compressible Darcy–Brinkman Model

Xiaoyu Zhu, Qihang Sun, Huizi Yang, Wei Liu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

A high-order algorithm targeting the two-dimensional semilinear compressible Darcy–Brinkman equation is proposed in porous media. This method combines block-centered and compact difference techniques in spatial discretization with the implicit-explicit (IMEX) fourth-order backward difference formula (BDF4) scheme for temporal discretization. The stability and error estimates for both the solution and flux of the provided scheme are demonstrated. Numerical experiments for model problems validate that this approach achieves fourth-order convergence in both space and time while exhibiting high accuracy and relatively ideal efficiency.

Optimal Control and Bayesian Parameter Estimation of a Nonlinear Compartmental Epidemic Model

Md. Harun‐Or‐Rashid Khan, Mostak Ahmed — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

Late blight, caused by the oomycete Phytophthora infestans, significantly threatens tomato cultivation. In this work, we propose a modified SEIR-type compartmental model with four epidemiological stages to capture the progression of the disease. A detailed mathematical analysis is carried out, establishing the model's positivity, boundedness, and the existence and stability of both disease-free and endemic equilibria. Parameter estimation is performed using Bayesian inference via Markov chain Monte Carlo (MCMC), ensuring consistency with empirical data. We then formulate and solve an optimal control problem using Pontryagin's maximum principle, aiming to reduce disease prevalence and control-related costs. The model incorporates a mobile app–based intervention strategy as a time-dependent control variable. This study highlights the effectiveness of combining rigorous mathematical modeling, data-driven calibration, and optimal control to inform the management of plant disease epidemics.

Breaking Waves and Solitary Waves for a Two‐Component Novikov System

Zhihong Li, Jian Chen, Shaojie Yang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we are concerned with two types of solutions of a two-component Novikov system, which is a coupled Camassa-Holm type system with cubic nonlinearity. The first type of solutions exhibits finite time singularity in the sense of wave breaking. We perform a refined analysis based on the local structure of the dynamics to provide a sufficient condition on the initial data to guarantee wave breaking. The other type of solutions which we investigate is solitary waves, we present the conditions for the existence of solitary waves.

An Accelerated Landweber Iteration Based on Barzilai–Borwein Step‐Size for Solving Nonlinear Inverse Problems

Yan Zhang, Jiangyan Zou, Meng Ji, Zhenwu Fu, Qinglong He — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

Iterative regularization methods are vital for solving mathematical physics inverse problems. Landweber iteration is one of the most well-known iterative regularization methods, whose most attractive property is its stability with respect to noise. However, its convergence speed is usually very slow, which greatly limits its widespread applications in practical problems. In this study, we propose an accelerated Landweber iteration based on Barzilai–Borwein (BB) step-size for solving nonlinear inverse problems. The convergence analysis of our proposed method is presented under standard assumptions. For validating the effectiveness of our method from the numerical computation point of view, the auto-convolution inverse problem based on integral equation and 1D, 2D parameter identification inverse problems based on elliptic equation are illustrated. Numerical results show that BB step-size can greatly accelerate Landweber iteration.

A Convergence Theorem for a Splitting Method and Its Applications in Geodesic Metric Spaces With Negative Curvature

Konrawut Khammahawong, Sakan Termkaew, Premyuda Dechboon, Urairat Deepan — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we study a splitting proximal method for minimizing the sum of convex functions defined on metric spaces with negative curvature. Our approach utilizes the resolvent operator and is tailored to the geometry of such spaces. We establish convergence rate theorems for the proposed splitting method by imposing additional conditions on the objective function. Finally, we apply our results to convex optimization problems arising in convex feasibility problems, the centroid problem, and, in particular, the computation of Karcher means.

Maximum Regularity of a Third‐Order Singular Nonlinear Equation

Mussakan Muratbekov, Madi Muratbekov, Akbota Abylayeva — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper investigates a nonlinear singular third-order equation with an unbounded coefficient at infinity. The existence and L2$$ {L}_2 $$-maximal regularity of solutions to the nonlinear equation are established. The method of ε$$ \varepsilon $$-regularization is applied in proving the existence of solutions. This approach has proven effective in the case of an unbounded domain with an unbounded coefficient.

On the Asymptotics of Attractors of the Ginzburg–Landau Complex Equation in a Perforated Domain With an Oscillating Boundary: Critical Case

Altyn Toleubay — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We analyze the asymptotic behavior of trajectory attractors associated with the Ginzburg–Landau complex equation in a perforated domain. This domain features a rapidly oscillating outer boundary. The analysis centers on the scenario in which the parameters defining the pore sizes, the distance between them, as well as the amplitude and frequency of the boundary oscillation, simultaneously approach zero. The asymptotic behavior of attractors related to an initial boundary value problem for complex Ginzburg–Landau equations in perforated domains, specifically in the critical case (which involves the emergence of additional potential in the homogenized equation), is examined by Bekmaganbetov K. A., Chechkin G. A., Chepyzhov V. V., and Tolemis A. A. This study is presented in their pape titled “Homogenization of Attractors to Ginzburg–Landau Equations in Media with Locally Periodic Obstacles:Critical Case”, Mathematics Series 3 no. 111 (2023): pp. 11–27 (published in the Bulletin of the Karaganda University). By defining the auxiliary function spaces with a weak topology, we derive a limit (homogenized) equation and prove the existence of a trajectory attractor for this equation. Subsequently, we formulate the main theorem regarding the weak convergence of attractors and prove it based on auxiliary lemmas.

Golden Ratio‐Inspired Subgradient Extragradient Algorithms With Increasing Self‐Adaptive Step Sizes for Solving Equilibrium Problems and Applications to Image Restoration

Habib ur Rehman, Nattawut Pholasa, Nuttapol Pakkaranang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

Equilibrium problems (EPs) provide a unified mathematical framework encompassing a broad class of models in optimization, variational inequalities, game theory, and applied sciences. In this paper, we propose two novel subgradient extragradient algorithms inspired by the golden ratio technique (GRT) for solving EPs in real Hilbert spaces. Both algorithms employ computationally efficient projections onto suitably constructed half-spaces rather than full projections onto the feasible set, thereby reducing the per-iteration computational cost. A key feature of our schemes is a self-adaptive step-size rule with increasing behavior, which updates the step sizes dynamically without requiring any prior knowledge of Lipschitz-type constants. The first algorithm integrates golden-ratio-based extrapolation with subgradient projection steps, while the second incorporates an alternating extrapolation mechanism to further enhance numerical stability and efficiency. Under standard assumptions, we establish weak convergence of the generated sequences to a solution of the EP, and we additionally prove R$$ R $$-linear convergence under stronger conditions. Extensive numerical experiments, including applications to image restoration, confirm that the proposed methods consistently outperform several existing extragradient-type algorithms in terms of convergence speed, accuracy, and stability.

Properties of the Solution of a Problem for a Pseudoparabolic Equation in a Non‐Cylindrical Domain

Myrzagali Ospanov, Akerke Merzetkhan — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we investigate a boundary value problem for a third-order pseudoparabolic equation posed in a non-cylindrical domain. Unlike most existing studies that are restricted to rectangular domains, our analysis focuses on a non-cylindrical domain with respect to the time variable, which requires the development of new techniques for treating nonlocal initial conditions. By applying the method of functional parametrization, we establish the existence and uniqueness of a solution and derive a series of a priori estimates for the solution as well as for its first- and mixed-order derivatives.

S‐Graphicable Algebras and Specific Graph Families

Manuel Ceballos — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper presents new developments in the relationship between S$$ S $$-graphicable algebras and graphs. Several general algebraic properties of S$$ S $$-graphicable evolution algebras are established, including characterizations of the annihilator, idempotent elements, and evolution subalgebras. It is also shown that S$$ S $$-graphicable algebras are non-solvable, and several results concerning their perfectness are provided. In addition, new families of S$$ S $$-graphicable algebras are introduced, each associated with well-known graph types, and the structural relationships among these families are analyzed, revealing significant algebraic connections. Finally, an algorithmic method is presented to determine whether a given evolution algebra is S$$ S $$-graphicable and, if so, to construct its associated graph.

About Solutions in the Broad Sense of Nonlinear Systems

Altynshash Bekbauova, Akylbek Meirambekuly — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

Using the method of characteristics this work investigates the existence of periodic solutions in the broad sense for nonlinear systems with non-uniform principal parts where the linear part does not decompose into independent homogeneous equations. Under the assumptions of continuity, boundedness and periodicity in some of the variables of the initial data, solutions in the broad sense are constructed. To study the solutions in the broad sense of a nonlinear system, nonlinear integral operators are constructed within a ball based on integral representations of solutions periodic in some variables for linear systems. The fixed-point principle is then applied to these operators.

On Sensitivity Analysis of A Nonlinear Mathematical Approach of Alcohol Consumption: A Piecewise Fractional and ANN Approach

Rimsha Tariq, Syeda Alishwa Zanib, Muhammad Farman, Manal Ghannam — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

One of the greatest challenges in public health is alcoholism, which impacts people from different socioeconomic backgrounds alike. The current research presents a mathematical model comprised of five compartments to depict the development of alcohol consumption and addiction. Nonlinear behaviour that is complex is noticed in actual drinking patterns, and memory effects are captured through the model's incorporation of Atangana–Baleanu (ABC) fractional derivatives. By employing the next-generation matrix method, the basic reproduction number R0$$ {R}_0 $$ is obtained and it is confirmed that the alcoholism-free equilibrium is locally stable for R0<1$$ {R}_0<1 $$. The Castillo–Chavez method then extends local stability to global asymptotic stability. The sensitivity analysis ranks dynamics of alcohol-use with parameters like alcohol-related mortality (g$$ g $$), population growth (ρ$$ \rho $$), transition and recovery rates (η,ξ,γ,f$$ \eta, \xi, \gamma, f $$), conversion rates (δ,σ,φ$$ \delta, \sigma, \varphi $$), and consumption levels as the most influential factors. To illustrate the varying population characteristics, three case studies are examined, each with a different set of parameters and reflecting various physiological and behavioural risk groups. Moreover, an Artificial Neural Network (ANN) is proposed in order to not only improve the computational efficiency but also offer variable numerical forecasts. The analytical and ANN-based numerical outcomes together provide a rich framework for the understanding and predicting of alcoholism's development.

Summation‐Integral Type Operators Associated With Frobenius‐Euler Polynomials

Deepak Bhardwaj, S. A. Mohiuddine, Arun Kajla, Abdullah Alotaibi — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this article, we construct a new class of summation-integral type positive operators linked with Frobenius-Euler polynomials. We obtain local approximation, Voronovskaya-type theorems and rate of convergence of these operators within a weighted function space. Also, the rate of convergence for functions with derivatives of bounded variation is established. Finally, we examine the convergence rates of the operators through graphical representations.

Temporal and Spatio‐Temporal Dynamics of Signaling Birds, Mammals and Its Predator With Anti‐Predator Behavior

R. P. Gupta, Shristi Tiwari — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In order to explore the interaction between a mammal and its predator, a model is formulated by incorporating mutualistic interactions between the signaling bird and the mammal. It is assumed that the signaling bird feeds on the parasites present on the mammal's body and that the mammals show anti-predator behavior towards their predator. We analyze the boundedness of the proposed system and establish the conditions for the existence and stability of ecologically feasible equilibrium states. The dynamical properties of the system, including the conditions for the occurrence of saddle-node, transcritical, and Hopf-bifurcation, are also investigated. To see the effect of signals, we obtain the conditions for the Hopf-bifurcation by assuming the signaling coefficients as bifurcation parameters. We also determine R0$$ {R}_0 $$ (the basic reproduction ratio) that represents a threshold parameter and determines whether the predators and their prey can coexist. We further show that if R0<1$$ {R}_0<1 $$, then the prey population may exist with signaling birds and the predator population goes extinct. If R0>1$$ {R}_0>1 $$, then all the three population may coexist. This analysis helps us to choose two critical parameters for which the bifurcations of codimension-2 may appear. The existence of Bogdanov–Takens and homoclinic bifurcations are ensured for suitable choices of parameters. To discuss the more natural scenarios, we further introduce diffusion in all three-species to capture their movement. The feasibility of solutions for the spatial model is derived. The conditions for Turing and non-Turing patterns are established with respect to the growth rate of birds, the saturation effect due to mammals and the signal given by birds to mammals. The corresponding patterns are plotted by using the five-point stencil method with random perturbation.

Nonlocal Kernel‐Driven Φ$$ \Phi $$‐Caputo Fractional Integro‐Differential Systems Involving the Generalized Laplace Transform

Asmaa Baihi, Samira Zerbib, Khalid Hilal, Ahmed Kajouni — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This study explores the existence and uniqueness of solutions for a fractional integro-differential equation of order ξ$$ \xi $$ involving a kernel operator. To construct the solution, we utilize the generalized Φ$$ \Phi $$-Laplace transform, which provides an explicit representation in terms of Mittag–Leffler functions and Φ$$ \Phi $$-convolutions. We establish the existence of solutions using Krasnoselskii's fixed point theorem, while uniqueness is proven through Banach's contraction principle. An illustrative example is included to demonstrate the applicability of our results.

Normalized Solutions for Kirchhoff–Choquard Equation With a Local Perturbation

Zi‐an Fan — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

The paper deals with the following problem: −(a+b∫ℝ3∇u2dx)Δu+λu=η∫ℝ3upx−yμdyup−2u+uq−2uinℝ3,∫ℝ3u2dx=c,u∈H1(ℝ3),$$ \left\{\begin{array}{l}-\left(a+b{\int}_{{\mathbb{R}}^3}{\left|\nabla u\right|}^2\mathrm{d}x\right)\Delta u+\lambda u=\eta {\int}_{{\mathbb{R}}^3}\frac{{\left|u\right|}^p}{{\left|x-y\right|}^{\mu }}\mathrm{d}y{\left|u\right|}^{p-2}u+{\left|u\right|}^{q-2}u\kern0.3em \mathrm{in}\kern0.3em {\mathbb{R}}^3,\\ {}{\int}_{{\mathbb{R}}^3}{\left|u\right|}^2\mathrm{d}x=c,u\in {H}^1\left({\mathbb{R}}^3\right),\end{array}\right. $$where (6−μ)/3<p<2μ∗$$ \left(6-\mu \right)/3<p<{2}_{\mu}^{\ast } $$, 0<μ<3,2<q≤2∗,c,η>0,λ∈ℝ$$ 0<\mu <3,\kern0.3em 2<q\le {2}^{\ast },\kern0.3em c,\eta >0,\kern0.3em \lambda \in \mathbb{R} $$. We establish the existence of normalized ground state solutions by using the Pohozaev manifold and subcritical approximation methods.

Exponential Stability of Impulsive Stochastic Functional Differential Equations With Delayed Impulses

Shuihong Xiao, Jianli Li — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper focuses on the exponential stability of impulsive stochastic functional differential equations (ISFDEs). First, we successfully attempt to establish a criterion for the practical pth$$ p\mathrm{th} $$ moment exponential stability (p$$ p $$-PES) of impulsive stochastic functional differential equations with delayed impulses (ISFDEDIs) using the newly established Halanay inequality. Furthermore, based on this inequality, we propose several sufficient conditions that have better applicability than the results in previous literature to ensure the system's pth$$ p\mathrm{th} $$ moment exponential stability (p$$ p $$-ES). Next, we derive a novel result that guarantees the p$$ p $$-ES of ISFDEDIs, based solely on the Lyapunov method. Additionally, using this approach, we establish a theorem on the generalized pth$$ p\mathrm{th} $$ moment exponential stability (p$$ p $$-GES) for impulsive stochastic functional differential equations with unbounded delays (ISFDEUDs). Notably, these results allow the decay rate to be equal to or less than the upper bound of the gain, which can address the limitations of the aforementioned results and existing studies in certain special cases. Finally, we present several examples to validate the effectiveness of our findings.

CMMSE Generalized Fourier Series Method for an Elastic Plate With a Multiply Connected Middle Plane Domain

Christian Constanda, Dale Doty — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

A generalized Fourier series method is constructed to approximate the solution of the Dirichlet problem in a finite domain with finitely many holes, in the case of bending of elastic plates with transverse shear deformation. The theoretical results are illustrated by an example with specific boundary conditions.

Stability of the One‐Species Vlasov‐Poisson‐Boltzmann System With Given Magnetic Field

Zhong Tan, Shihan Zhao — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we focus on the one-species Vlasov-Poisson-Boltzmann system under a given magnetic field with nonconstant background density in the whole space. We first give the existence of a stationary solution when the background density is a small perturbation of a constant state. Secondly, we establish the nonlinear stability of the Cauchy problem near the stationary solution in certain Sobolev spaces. The proof relies on macroscopic balance laws and several interactive energy functionals from [1], extending the results in [1] to the magnetized case and demonstrating that a constant magnetic field does not affect the nonlinear stability of the stationary solution.

From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics

Carlos Lizama, Marina Murillo‐Arcila, Julio Puerta‐Fernández — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We investigate the transition between stability and chaos in the damped Klein-Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics, including Devaney and distributional chaos as well as topological mixing. The results yield a classification of the dynamical regimes in terms of damping, stiffness, and propagation parameters, showing that the system admits only two long-term behaviours: Convergence to equilibrium or chaos. This dichotomy not only unifies and extends previous partial results but also highlights the mechanisms by which linear partial differential equations can generate complex dynamics typically associated with nonlinear systems. Potential applications arise in acoustics, wave mechanics, and signal transmission, where predicting the onset of chaos versus stability is of practical importance.

Existence and Decay of Mild Solutions for the Time‐Space Fractional Burgers Equations

Xingmei Feng, Yong Zhou — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This study investigates the Cauchy problem related to the time-space fractional Burgers equation, expanding on the classical Burgers equation by substituting the standard integer-order time derivative with the Caputo fractional-order derivative and replacing the classic Laplacian with a fractional Laplacian. The research employs fractional heat kernel estimates and the Mittag–Leffler function to establish initial estimates for solution operators, focusing on both local and global mild solutions within Lebesgue spaces and their decay properties. The main proof leverages the fixed-point theorem, offering new theoretical perspectives on fractional Burgers equations.

Symmetries, Bifurcations and Control for Traveling Waves of the Drinfeld‐Sokolov‐Wilson System

Chenxin Luo, Lin Lu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we employ the Lie symmetry method to derive the Lie infinitesimal generators for the Drinfeld-Sokolov-Wilson system. By symmetry reduction, the original partial differential equation (PDE) system is transformed into an ordinary differential equation (ODE) system. We analyze the equilibrium points and phase portraits of the resulting planar dynamical system. By using bifurcation theory, we construct various types of traveling wave solutions, including smooth periodic waves, bounded soliton waves, kink and anti-kink waves, periodic blow-up solutions, and blow-up solitons. Furthermore, based on the differential geometry structure, we design a feedback continuous controller to globally stabilize the traveling waves at equilibrium points. Moreover, we perform numerical simulations to validate the analytical results.

Local Well‐Posedness of a Perturbed Problem for the Abels–Garcke–Grün Model in Three Dimensions

Maoyin Lv — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We investigate the Abels–Garcke–Grün model that describes the motion of two viscous incompressible fluids with unmatched densities in the presence of a uniform gravitational field. For the perturbed system with respect to a given equilibrium state in three dimensions, we establish the local existence and uniqueness of a strong solution using a suitable iteration scheme and the energy method. This work lays the foundation for further studies on the Rayleigh–Taylor instability problem of nonhomogeneous two-phase flows within the framework of diffuse interface models.

Bound States of a Non‐Hermitian System With a QES Sine Potential via AIM

H. F. Kisoglu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this study, the eigenfunctions (wavefunctions) of a non-Hermitian system defined by a complex periodic sine potential are obtained in the form of a hypergeometric series, while its real eigenvalues are derived in closed form. To this end, the one-dimensional Schrödinger equation is formulated for a PT-symmetric system of this type, and asymptotic iteration method is employed as the mathematical tool. Owing to the method's applicability to quasi-exact, numerical, or perturbative regimes, the obtained real analytical eigenvalues are shown to be in good agreement with the literature. Accordingly, a specific condition on the potential parameters, determined by means of the method, indicates that the wavefunction can be expressed in the form of a hypergeometric series. Furthermore, the method demonstrates that the analytical eigenvalues (and the corresponding wavefunction) remain valid, particularly at high-energy levels, even when the potential parameters deviate from this specific condition. Additionally, the obtained wavefunctions are shown to be consistent with Bloch's theorem in solid-state physics.

Hybrid Methods of Series Decomposition and Legendre Collocation for the Emden‐Fowler Equation With Blow‐Up

Yuxuan Wang, Zhifang Liu, Tongke Wang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper proposes a series decomposition algorithm and two Legendre collocation methods to solve the Emden-Fowler equation with probably non-smooth or blow-up solution. By reformatting the equation into an equivalent integral form, we derive a psi-series solution that includes logarithmic polynomials via successive iteration, which achieves high accuracy near the origin. By cutting off a small interval containing the singularity, we develop the Legendre collocation methods in both integral form with Legendre-Gauss points and differential form using Legendre-Gauss-Radau points to solve the problem on the regular interval. We also prove the convergence of the Legendre-Gauss method in integral form. For the blow-up problem, we apply the Padé technique to the series solution to evaluate the blow-up time and discuss the blow-up behavior of the solution. We then improve the accuracy of the Legendre collocation methods by removing the blow-up singularity from the equation. Several examples illustrate that the hybrid methods in this paper can achieve high accuracy for the Emden-Fowler equation with initial conditions.

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid-state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II-A equation, a relatively less-explored parametric nonlinear partial differential equation that describes nonlinear wave propagation and soliton dynamics in diverse physical systems. To address the gap in analytical and numerical treatments of this equation, we derive new exact soliton solutions using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$-expansion method, yielding exponential, trigonometric, and rational solution forms. Moreover, we introduce a novel hybrid framework by applying regularization-based backpropagation neural networks to approximate these solutions numerically. This dual approach, combining symbolic analysis with machine learning, offers a robust means to validate and extend analytical findings. The originality of this work lies in presenting, for the first time, a unified analytical-neural network framework for solving the Shynaray II-A equation, which has not been systematically studied in prior literature. Comparative error metrics and visualization confirm the accuracy and efficiency of the proposed method, providing new insights into the behavior of nonlinear wave systems and demonstrating the potential of hybrid soliton modeling strategies.

Direct and Inverse Problems for Nonlocal Diffusion Equation in ℝ3$$ {\mathbb{R}}^3 $$

Sehrish Javed, Salman A. Malik — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We considered the direct problem (DP) and inverse problem (IP) of determining a reaction coefficient of the diffusion equation involving Dzherbashian-Nersesian integro-differential operator (DNIDO). The solutions of direct and IPs are written in the form of Fox H-function. The reaction coefficient is supposed to depend only on the first two components of the spatial variable y=(y1,y2,y3)∈ℝ3$$ y=\left({y}_1,{y}_2,{y}_3\right)\in {\mathbb{R}}^3 $$ and on the time variable t$$ t $$. The over-specified condition for the IP is the projection of diffusion concentration in the y1y2$$ {y}_1{y}_2 $$-plane. The IP is reduced to an equivalent integral equation (IE), and existence and uniqueness for the solution of the IP is proved by applying the Banach fixed point theorem (BFPT). The stability of the solution of the direct and IPs, when diffusion coefficient, source term, and initial data are perturbed, is proved and some examples are provided. We have generalized our main problem from ℝ3$$ {\mathbb{R}}^3 $$ to ℝn$$ {\mathbb{R}}^n $$. Some numerical examples with an exponentially decaying source and periodic reaction coefficient term are presented.

Monotonicity of Positive Solutions for Dual Fractional Parabolic Equation Involving Fully Nonlinear Nonlocal Operator

Zerong Yang, Jialin Li, Yong He, Wei Zhang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this article, we investigate the monotonicity of positive solutions for fully nonlinear fractional order parabolic equations involving the fractional time derivative by applying the moving planes method. We first establish a series of key theorems in the proofs, such as narrow region principles and averaging effects. Then, we use these tools to demonstrate the monotonicity of positive solutions in a half-space.

Solutions Construction for the gcmKP Hierarchy via Boson‐Fermion Correspondence

Wenchuang Guan, Jinbiao Wang, Jia Yangjie, Shen Wang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper focuses on the generalized constrained modified Kadomtsev–Petviashvili (gcmKP) hierarchy. First, we utilize the boson-fermion correspondence to transform the Hirota bilinear equations of the gcmKP hierarchy into fermionic form. Based on this representation, we construct explicit rational and soliton solutions by selecting specific group elements in the Lie group GL(∞)$$ GL\left(\infty \right) $$, expressing them as vacuum expectation values and presenting concrete examples.

Analysis of Hopf Bifurcation and Chaos in a Class of Duffing Systems

Shuai Zhu, Jiaquan Xie, Wei Shi, Jiamin Tian, Jiale Zhang — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper focuses on a class of Duffing systems characterized by the presence of a sign function. The study provides a theoretical analysis of the system from a mathematical perspective, categorizing it into three distinct types based on the range of the sign function. Utilizing the KBM method, approximate analytical solutions for these categorized systems are derived. The Hurwitz criterion is employed to conduct a stability analysis of the classified systems, leading to the conclusion that Hopf bifurcation does not occur within the system. Furthermore, through the study of Homoclinic Trajectories, energy curves, and phase diagrams, the system is theoretically analyzed and numerically simulated. The results confirm that the system does not exhibit chaos induced by the cross-intersection of Homoclinic Trajectories.

Super‐Subsolution Methods for Nonlocal Problems With Semipositone Nonlinearities

Rafik Guefaifia, Salah Boulaaras, Abdelaziz Sabiry — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper, we investigate a class of nonlocal Kirchhoff-type problems in Orlicz–Sobolev spaces, involving strongly perturbed singular terms and Heaviside-type discontinuous nonlinearities. By combining the monotone operator theory with the method of super- and subsolutions, we establish the existence and multiplicity of positive solutions. Our results extend previous works on Θi$$ {\Theta}_i $$-Laplacian and nonlocal Kirchhoff problems by addressing more general nonlinearities, including semipositone and concave-convex cases. Several illustrative examples are provided to demonstrate the applicability of our approach.

Mathematical Investigation of Optimal Control of a Tumor Growth Model Drug Administration

Zeinab Joorsara, S. M. Hosseini, Sakine Esmaili — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This study investigates the optimal control problem for tumor growth dynamics, focusing on the existence and uniqueness of solutions. We derive necessary optimality conditions and prove the optimal control exists and is unique using the fixed-point theorem. As our objective function includes weighted L2$$ {L}^2 $$- and L1$$ {L}^1 $$-norms of controls, we first establish the existence and uniqueness of optimal control for L2$$ {L}^2 $$-type problem and derive its optimal control form. Furthermore, due to the aggressive nature of the cytotoxic drug and the importance of determining its optimal dose during treatment, we considered the objective function to be linear with respect to this drug and referred to it as an L1$$ {L}^1 $$-type problem. Next, we illustrate the relationship between the solutions of L2$$ {L}^2 $$-type and L1$$ {L}^1 $$-type problems. Additionally, using the Pontryagin Minimum Principle for L1$$ {L}^1 $$-type optimal control problem, we demonstrate numerically that the resulting optimal control is nonsingular. The relationship between the optimal control obtained from solving the problem directly and the results from its analytical solution is numerically demonstrated.

The Linearized Inverse Boundary Value Problem in Strain Gradient Elasticity

Antonios Katsampakos, Antonios Charalambopoulos — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this paper we study the linearized version of the strain gradient elasticity equation in ℝ2$$ {\mathbb{R}}^2 $$ with constant coefficients and we prove that one can determine the two Lamé coefficients λ,μ$$ \lambda, \mu $$ as well as the internal strain gradient parameter g$$ g $$, as indicated by Mindlin in his revolutionary papers in 1963–1965, by boundary measurements. This is accomplished via the investigation of the corresponding Steklov-Poincaré operator, which, in the current situation, stems from a fourth order boundary value problem and merits several qualitative differences in comparison to the classical elasticity problem. The investigation of the Fréchet derivative of this operator is the cornerstone in the realm of the solvability of the inverse problem.

Recovering Initial Values and a Random Source Simultaneously for a Damped Wave Equation

Kuijian Chang, Yuxuan Gong, Xiang Xu — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper introduces an inverse problem for a stochastic damped wave equation, in which the source is driven by a fractional Brownian motion. The well-posedness of direct problem is obtained by analyzing regularity of the solution for the equivalent stochastic initial value problem in frequency domain. The inverse problem involves recovering two initial values and a random source simultaneously. It is shown that the mean of final observations at two different moments uniquely determines the initial values. Additionally, for inversion of random source, it is demonstrated that its sine modulus can be uniquely determined by the variance of final observations. Based on this sine modulus, recovering the unknown random source can be transformed into a well-known phase retrieval problem, which can be successfully solved using the methodology of phaselift. Finally, numerical examples are presented to demonstrate the effectiveness of this method.

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Ibrahim Ahmad Suleman, Mokhtar Kirane — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u\left(0,x\right)=\varphi (x),\kern0.60em {u}_t\left(0,x\right)=\psi (x), $$ which we derive particularly to observe the roles of ε$$ \varepsilon $$ and β$$ \beta $$ in the long time behavior of solutions. Moreover, we apply these estimates to obtain local in time weak solutions, and global solutions, under the influence of a nonlocal non-power nonlinear term.

Modeling Distributed Denial‐of‐Service Attacks to Develop Defensive Strategies in the Internet of Everything

Pongsarun Boonyopakorn, Mahasak Ketcham, Thittaporn Ganokratanaa — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

As smart devices become increasingly interconnected through the Internet, the Internet of Everything (IoE) has emerged as a foundational aspect of modern life, supporting convenience, automation, and energy management. However, many IoE devices lack sufficient security mechanisms, making them vulnerable targets for cyberattacks, particularly Distributed Denial-of-Service (DDoS) attacks. This research proposes a mathematical modeling framework to analyze and simulate the behavior of DDoS attacks in IoE environments. A modified SIR (Susceptible-Infected-Recovered) model is employed to represent device state transitions, combined with assumptions about traffic volume and device capacity, as well as theoretical theorems for developing effective defense strategies. Simulation results reveal that when the basic reproduction number R0=β/γ$$ R0=\beta /\gamma $$ exceeds 1, the system experiences rapid propagation of the attack, with the number of compromised devices increasing significantly before recovering through isolation mechanisms. Three defense strategies were compared: no defense, static defense with δ=0.33$$ \delta =0.33 $$, and adaptive defense that adjusts dynamically based on the infection level. The results show that without defense, the system is overwhelmed and fails. Static defense fully mitigates the attack but consumes a constant level of resources. In contrast, adaptive defense effectively reduces system impact using significantly fewer resources by scaling mitigation based on real-time threats. Visualizations such as phase diagrams, heatmaps, and cumulative cost graphs confirm the theoretical findings and illustrate the dynamics clearly. This study concludes that mathematical modeling, combined with dynamic control strategies, can significantly improve the resilience of IoE systems against DDoS attacks. The validated approach offers a practical foundation for designing scalable and adaptive cybersecurity solutions for future IoT and IoE infrastructures.

Estimates of Approximation Numbers and Completeness of Root Vectors of A Singular Operator Generated by the Linear Part of the Korteweg‐de Vries Operator

Mussakan Muratbekov, Madi Muratbekov, Yerik Bayandiyev — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

We investigate a linear operator associated with the linear part of the Korteweg-de Vries operator on an unbounded domain with unbounded coefficients. The existence and compactness of the resolvent are established, along with separability results ensuring maximal regularity of solutions. Two-sided estimates are derived for the distribution function of approximation numbers, characterizing the rate of finite-dimensional approximation of the resolvent. The completeness of the system of root vectors is also proved, which plays a key role in the analysis of related nonlinear operators.

Analysis of Cylindrical Membrane Effects on Shear‐Horizontal Wave Propagation in PFRC Core–Shell Structures

Bikram Dholey, Kshitish Ch. Mistri, Gopal Chandra Shit, Amrita Das — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper presents a comprehensive investigation of shear-horizontal (SH) wave propagation in a novel cylindrical core-shell structure composed of a piezoelectric fiber-reinforced composite (PFRC) core encased by a concentric isotropic elastic shell. Three different types of imperfect interfaces are examined in detail: (a) a spring interface, (b) a membrane interface, and (c) a spring–membrane combined interface. The analysis, carried out in cylindrical coordinates, focuses on circumferential wave motion relevant to advanced structural and biomedical applications. The anisotropic behavior of the PFRC core, derived from the micro-mechanical arrangement of aligned piezoelectric fibers in an epoxy matrix, is fully incorporated, while the isotropic coating provides the necessary mechanical contrast to highlight interfacial effects. A thin cylindrical elastic membrane is introduced to replicate interfacial bonding or compliant layers typically observed in layered manufacturing and implantable devices, where its presence induces mode conversion and significantly modifies wave dynamics. A coupled electromechanical model is formulated, and dispersion relations for guided SH modes are derived using variable separation methods with Bessel and Hankel functions. The model is validated through limiting cases. Parametric studies investigate the influence of core–shell radii, spring stiffness, membrane density and elastic constant, and PFRC fiber volume fraction. Numerical results, illustrated through dispersion curves, 3D surface plots, and time-dependent fields of displacement and electric potential, demonstrate how the three interface models distinctly affect wave behavior. The study highlights the potential of interface-engineered cylindrical composites for tunable SH-wave propagation and tailored electromechanical response.

On the Existence and Long‐Time Behavior of Solutions to Swelling Models With Weak Logarithmic Damping Mechanism: Optimal Polynomial Decay Rate

Adel M. Al‐Mahdi, Mohammed M. Al‐Gharabli — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

In this work, we investigate a nonlinear swelling problem subject to only one weak logarithmic damping of the form sgn(zt)ln1+|zt|$$ \operatorname{sgn}\left({z}_t\right)\kern0.3em \ln \kern0.3em \left(1+|{z}_t|\right) $$ acting on the fluid equation. We establish the global existence of strong solutions by employing the Galerkin method in conjunction with compactness arguments, thereby providing a rigorous mathematical framework for the well-posedness of the model. Furthermore, by applying the multiplier method, we derive a general decay estimate for the associated energy functional. The obtained decay rate is shown to be faster than any polynomial rate yet slower than the exponential one, which represents the optimal decay behavior achievable under this weak logarithmic dissipation. These results not only shed light on the intricate interplay between swelling dynamics and logarithmic feedback mechanisms but also open new avenues for future investigations of related systems governed by such unconventional damping laws.

Adaptive Fixed‐Time Bipartite Containment Control for Saturated Nonlinear Multi‐Agent Systems Based on Optimized Backstepping Technique

Li Tang, Huanqing Wang, Xudong Zhao, Ning Xu, Lun Li — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This paper studies the fixed-time optimal bipartite containment control problem for nonlinear multi-agent systems (MASs) with input saturation. First, the conventional bipartite containment problem is reformulated as an optimal control problem on the communication topology by constructing a performance cost function that incorporates both control inputs and tracking errors. Then, a novel identifier–actor–critic reinforcement learning (RL) architecture based on neural networks (NNs) is developed to solve the Hamilton–Jacobi–Bellman (HJB) equation online without requiring prior knowledge of system dynamics. In addition, an auxiliary system is designed to compensate for the negative effect of input saturation, enabling reliable control under actuator constraints. Subsequently, a fixed-time optimal controller is proposed to ensure that tracking errors converge to a small domain near the origin in a fixed time with minimal cost, and all the closed-loop signals are bounded. Finally, two examples are used to illustrate the effectiveness of the proposed control method.

Nonlinear Wave Equation With Infinite Memory: Analyzing Stability and Blow‐Up Under Fractional Boundary Delay

Luqman Bashir, Jianghao Hao, M. Fahim Aslam — Mon, 18 May 2026 01:52:58 -0700

ABSTRACT

This study investigates a nonlinear wave equation defined on a bounded and smooth domain Ω⊂ℝn$$ \Omega \subset {\mathrm{\mathbb{R}}}^n $$, incorporating infinite memory and a nonlinear source term, together with a boundary condition that involves both a tempered Caputo fractional time-varying delay and a linear damping effect. Local existence of solutions is established using semigroup theory, while the global existence is proved through the energy method. The exponential stability analysis is carried out by constructing a suitable Lyapunov functional and a finite-time blow-up result is derived when the initial energy is negative. To the best of our knowledge, this is the first study to address such a configuration within the framework of wave equations.

A High‐Order Reaction‐Diffusion Coupled System for Super‐Resolution

K. Jenkal, Z. Zaabouli, L. Afraites, A. Laghrib — Fri, 15 May 2026 18:10:21 -0700

ABSTRACT

Super-resolution (SR) remains a critical challenge in imaging science, particularly in applications demanding fine-texture reconstruction and noise suppression. In this work, we introduce a novel nonvariational anisotropic diffusion model, formulated as a high-order nonlinear reaction-diffusion system, designed to enhance SR capabilities. Our approach utilizes a decomposition strategy based on the H−1$$ {H}^{-1} $$ norm, which effectively captures and preserves fine details and intricate textures in images. Theoretical analysis establishes the well-posedness of the model via the Schauder fixed-point theorem, ensuring mathematical rigor. To validate its performance, we implement a finite difference numerical scheme, testing the model against state-of-the-art SR techniques on challenging image datasets. Results demonstrate significant improvements in texture restoration, edge sharpness, and robustness to noise and degradation, surpassing competitive methods. This research lays the foundation for advanced PDE-based SR frameworks, offering significant potential for applications in biomedical imaging, satellite vision, and high-fidelity computational photography.

Normalized Solutions for Fractional Kirchhoff–Choquard Equations

Zhenyu Guo, Tongtong Guo — Fri, 15 May 2026 02:09:44 -0700

ABSTRACT

In this paper, we study a class of fractional Kirchhoff-Choquard equations with fixed mass constraints in ℝ3$$ {\mathbb{R}}^3 $$. Based on the Pohozaev manifold, by establishing the compactness lemma of the Palais–Smale sequence and using Ekeland variational principle, the existence of solutions is obtained and their asymptotic behavior is analyzed for s∈34,1$$ s\in \left(\frac{3}{4},1\right) $$. Through variable substitution, the low-order fractional Kirchhoff equation is transformed into an equivalent system. Combining fractional inequalities and variational methods, the existence of solutions is obtained for s∈0,34$$ s\in \left(0,\frac{3}{4}\right] $$.

Existence and Stability of Traveling Wavefronts in a Diffusive Vector Disease Model With Nonlocal Distributed Delay

Cun‐Hua Zhang, Xiang‐Ping Yan — Fri, 15 May 2026 00:17:22 -0700

ABSTRACT

This article is concerned with the traveling wave front solutions of a vector disease model with a nonlocal distributed delay incorporated as an integral convolution over all past time and the whole one-dimensional spatial domain ℝ$$ \mathbb{R} $$. In the situation when the delay kernel is assumed to be the strong generic kernel and the kernel parameter is sufficiently small, the existence and the exponential stability of traveling wavefront solutions are separately established by using the linear chain techniques and the geometric singular perturbation theory, as well as the comparison principle and the weighted energy estimates in a suitable weighted space.

2D Impulsive Pseudoparabolic Equations With the Volterra‐Type and Fredholm‐Type Initial Layers

Stanislav Antontsev, Ivan Kuznetsov, Sergey Sazhenkov — Fri, 15 May 2026 00:02:10 -0700

ABSTRACT

We study the two-dimensional Cauchy–Dirichlet problems for the quasilinear pseudoparabolic integro-differential Volterra equation and for the quasilinear pseudoparabolic integro-differential Fredholm equation. In each of these two problems, the integral term depends on a positive integer parameter n$$ n $$ and, as n→+∞$$ n\to +\infty $$, converges weakly⋆$$ {}^{\star } $$ to the expression incorporating the Dirac delta-function, which models an instantaneous impulsive impact. For fixed n∈ℕ$$ n\in \mathbb{N} $$ we prove the well-posedness of each of the two problems in the class of regular weak solutions. Further, for each of the two problems, we establish that the initial shock layer, associated with the Dirac delta-function, is formed as n→+∞$$ n\to +\infty $$, and that the family of regular weak solutions of the original problem converges to the strong solution of a limit two-scale microscopic–macroscopic model.

Analysis of the Fractional Mathematical Model for Lung Cancer Dynamics With the Effects of Chemotherapy, Hypoxia, and Immunotherapy

Fri, 15 May 2026 00:00:00 -0700

ABSTRACT

The study strives to formulate and examine a fractional nonlinear dynamic model of lung cancer that integrates the impacts of chemotherapy, hypoxia, and immunotherapy. The presence and uniqueness of the fractional lung cancer model have been shown. The Hyers–Ulam stability of the lung cancer model is examined as well. A lung cancer model has been assessed quantitatively using the Atangana–Toufik methodology. A computer simulation demonstrates that chemotherapy, hypoxia, and immunotherapy significantly reduce the dissemination of lung cancer to other regions.

Effects of Random Diffusion and Advection on a Predator–Prey Model

Yu‐Xia Wang, Peng‐Xiang Zhang — Thu, 14 May 2026 07:18:06 -0700

ABSTRACT

In this article, we investigate the steady state problem of a predator–prey model incorporating random diffusion and advection under homogeneous Dirichlet boundary conditions. To gain a better understanding of random diffusion and advection, the stability of semitrivial steady state solutions, the nonexistence and existence of positive steady-state solutions are given. The results indicate that diffusion has a significant influence on both the stability of semitrivial steady state solutions and the coexistence region. In particular, a small positive advection coefficient reduces the size of the coexistence region, whereas a large positive advection coefficient may lead to bistable phenomena. Moreover, as other parameters vary, the stability of one semitrivial steady state solution may change at least twice.

Maximum Principles for a Caputo–Katugampola Fractional Differential Equation in a Network

J. Caballero, J. Harjani, K. Sadarangani — Thu, 14 May 2026 06:00:34 -0700

ABSTRACT

In this article, we obtain some extremum principles for a fractional differential equation involving the Caputo–Katugampola derivative of order 0<α<1$$ 0<\alpha <1 $$ in a network. Moreover, we prove results about the uniqueness and continuity of solutions with respect to the initial data.

Statistical Soliton on Statistical Perfect Fluid Space‐Time

Fatemeh Asali, Mohammad Bagher Kazemi Balgeshir — Wed, 13 May 2026 06:54:16 -0700

ABSTRACT

In this paper, we introduce the perfect fluid space-time, soliton, and concircular vector field of a statistical manifold. We explore both geometric and physical properties of statistical perfect fluid space-times under a framework of almost statistical solitons. We prove key results related to the divergence of almost statistical solitons vector fields. Explicit relations of differentiable functions, conditions associated with the statistical concircular vector fields, are stated. Also, the interaction of statistical solitons conditions with vector fields associated with a statistical Ricci curvature is investigated, and constraints on scalar fields and curvature tensors are obtained.

Dynamical Analysis of A Predator‐Prey Model Incorporating Allee Effect and Mutual Interference Between Predators

Chenyu Wang, Wensheng Yang — Wed, 13 May 2026 03:21:07 -0700

ABSTRACT

In this paper, we put forward and study a modified Leslie-Gower predator-prey model with Crowley-Martin functional response and Allee effect in the growth rate of a predator population. Crowley–Martin-type functional response is considered to describe mutual interference between predators. Our analysis shows that the intensity of Allee effect affect the stability of all equilibria, and by plotting the two-parameter bifurcation diagram of the degree of mutual interference between predators and the intensity of Allee effect, it is found that under their influence, the system will appear Bi-stable phenomenon. In addition, by considering the intensity of Allee effect as a bifurcation parameter, the one-parameter bifurcation diagram of the predator appears saddle-node bifurcation and Hopf bifurcation. Finally, Turing instability occurs in the reaction-diffusion system. The study reveals that as the intensity of the Allee effect increases, predators face greater survival pressure, their population growth becomes limited, predation patterns changes, the distribution of the prey population changes, and low-density areas of the prey decrease. As mutual interference between predators increases, the distribution patterns of both predators and prey shift significantly. High interference reduces high-density prey clusters, while predator distribution, though fluctuating, becomes smoother overall. This study highlights the complex interaction between Allee effect and predator-predator interaction in predator-prey dynamics. The results may provide biological insights and ecological management suggestions for predator-prey interaction.

Non‐Stationary Helical 3D Rivulet‐Flows of Viscous‐Plastic Incompressible Non‐Newtonian Fluid

S. V. Ershkov, E. S. Baranovskii, A. V. Yudin — Wed, 13 May 2026 00:41:51 -0700

ABSTRACT

The novel case of nonstationary flows of helical type governed by gravity-driven viscous-plastic flow dynamics derived for incompressible non-Newtonian fluid is investigated here analytically in case of given (constant) value of Bernoulli-function. In such types of flow, the velocity is linearly and spatially dependent on curl field. Conditions for the existence of the exact solution for the aforementioned type of flows are obtained. Equations of momentum, continuity, and that one for the components of stress tensor are studied. The spatial and time-dependent structure of pressure field of the fluid flow should be determined via constant Bernoulli-function if components of the velocity of the flow are already obtained. It is remarkable that the case of non-stationary helical or Beltrami flow for incompressible gravity-driven viscous-plastic flow governed by three-dimensional equations has been investigated for the first time to the best of our knowledge.

MSC Classification: 35Q35, 76D17

Analytical and Numerical Investigations on the Existence and Stability of Fractional p$$ p $$‐Laplacian Equations Subject to Integral Boundary Conditions

Faouzi Haddouchi — Tue, 12 May 2026 05:14:59 -0700

ABSTRACT

This work aims to carry out a detailed investigation on the existence, uniqueness, and stability of the solutions of p$$ p $$-Laplacian Caputo fractional differential equations with integral boundary condition. To begin, the properties of the associated Green's functions are derived. Next, the existence and uniqueness of the solutions are then examined by employing two classical fixed point theorems. Additionally, we verify that the formulated problem preserves its stability in the sense defined by Ulam–Hyers. Examples including tables and figures with numerical results are provided to illustrate the applications of our findings.

Bifurcation Dynamics of a Pest Management System With Cooperative Predation, Fear Effect, and Impulsive Density‐Dependent Nonlinear Effects

Zeli Zhou, Jianjun Jiao, Bingying Gao — Mon, 11 May 2026 00:25:05 -0700

ABSTRACT

Effective integrated pest management should control pests while safeguarding the environment and human health. This study proposes a novel pest management system incorporating cooperative predation, fear effect, impulsive density-dependent nonlinear prey (pest) trapping and predator (natural enemy) release. The conditions for global asymptotic stability of the prey extinction periodic solution and system permanence are established. A supercritical bifurcation occurs when the impulsive control period serves as a bifurcation parameter. This implies that a transition from a prey extinction periodic solution to a positive periodic solution of prey–predator coexistence when the impulsive period exceeds a critical value. Meanwhile, simulations are conducted to verify the theoretical results, determine the key factors influencing pest extinction threshold condition, and explore the complex dynamics of the system. This analysis will aid future research and the development of effective pest control strategies.

A Prüfer Angle Approach to Dependence of Eigenvalue for Sturm‐Liouville Problem With Distributional Potentials

Gaofeng Du, Chenghua Gao — Sun, 10 May 2026 21:42:06 -0700

ABSTRACT

In this paper, we apply the Prüfer transformation to investigate the dependence of eigenvalues for the Sturm–Liouville problem with distributional potentials. Based on several important properties of Prüfer angle established herein, the precise oscillation theorems for the problem are obtained. Moreover, it is proved that the eigenvalue functionals are not only completely continuous but also continuously differentiable in potentials. Meanwhile, we derive the precise Fréchet derivative formula of eigenvalue in potentials.

Inverse Nodal Problems for Discontinuous Sturm–Liouville Operators and Their Numerical Solutions

Yu Ping Wang, Chung‐Tsun Shieh, Shahrbanoo Akbarpoor — Fri, 08 May 2026 06:34:18 -0700

ABSTRACT

In this paper, we study the direct and inverse problems for discontinuous Sturm–Liouville operators. Firstly, we obtain exact asymptotes of eigenvalues with the oscillating and nodal points (i.e., zeros) of the eigenfunctions. Then, we propose some valid numerical methods to study numerical solutions of the inverse nodal problems for this operator and present a comparison of the numerical methods. Finally, we show that the potential q(x)$$ q(x) $$ is uniquely determined by the dense nodal subset on [0,1]$$ \left[0,1\right] $$. In particular, applying the Bernstein method, we reconstruct the potential q(x)$$ q(x) $$ from only a nodal subset.

Riemann–Hilbert Problem and Inverse Scattering Analysis for a New Generalized Variable‐Coefficients Pavlov System

Linlin Gui, Yufeng Zhang — Fri, 08 May 2026 06:33:06 -0700

ABSTRACT

In this paper, we introduce a pair of two-dimensional non-isospectral vector fields whose commutation gives rise to a new variable-coefficients integrable system which can reduce to the well-known Pavlov equation. We refer to the new integrable system as the (2 + 1)-dimensional generalized variable-coefficients Pavlov (gVCP) system: (a) studying the inverse scattering and Cauchy problems via the inverse scattering transform (IST); (b) constructing the localized solutions of the gVCP via the Riemann–Hilbert (RH) method; (c) analyzing the large t$$ t $$ behavior of the solutions of the Cauchy problem for the gVCP system; (d) characterizing a class of implicit solutions of the gVCP system.