Mathematical Methods in the Applied Sciences最新文献

{"title":"Development of Chelyshkov Wavelets Neural Network Method for Solving Nonlinear Fractal–Fractional Optimal Control Problems","authors":"Parisa Rahimkhani,&nbsp;Seydi Battal Gazi Karakoc,&nbsp;Thabet Abdeljawad","doi":"10.1002/mma.70839","DOIUrl":"https://doi.org/10.1002/mma.70839","url":null,"abstract":"<div>\u0000 \u0000 <p>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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15517-15533"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Stability of a Diffusive Leslie-Gower Type Model With Intraspecific Competition","authors":"Norberto Aníbal Maidana","doi":"10.1002/mma.70832","DOIUrl":"https://doi.org/10.1002/mma.70832","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this work is to improve the global stability results for reaction-diffusion Leslie-Gower type models in a bounded domain <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>∈</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ Omega in {mathbb{R}}^n $$</annotation>\u0000 </semantics></math>, 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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15473-15494"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Dynamics of a CTL Immune Response Delayed Virus Infection Model With Lytic and Nonlytic Effector Mechanisms","authors":"Zhipeng Xu,&nbsp;Wanbiao Ma","doi":"10.1002/mma.70843","DOIUrl":"https://doi.org/10.1002/mma.70843","url":null,"abstract":"<div>\u0000 \u0000 <p>This study investigates a class of delayed virus infection model that incorporates CTL immune responses with both lytic and nonlytic effector mechanisms. The model incorporates two delays: an intracellular delay <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {tau}_1 $$</annotation>\u0000 </semantics></math> and a CTL immune response delay <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>τ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {tau}_2 $$</annotation>\u0000 </semantics></math>. By fully leveraging the expressions of the model's two threshold parameters <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {R}_0 $$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {R}_1 $$</annotation>\u0000 </semantics></math>, constructing appropriate Lyapunov functionals, and employing sophisticated inequality analysis techniques, we establish the following results: (i) the global asymptotic stability (GAS) of the infection-free equilibrium is completely obtained; (ii) the sufficient conditions for the GAS of the immune-free equilibrium are derived; (iii) under specific parameter constraints, the sufficient conditions for the GAS of the immune activation equilibrium are obtained. The results in this paper further extend the conclusions in the existing literature. Meanwhile, the model is applied to experimental data from humanized mice infected with HIV-1, demonstrating the effectiveness of the model in predicting empirical data.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15730-15752"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy Shaping of Distributed Port-Hamiltonian Systems Based on Finite Volume Approximation","authors":"Fu Zheng,&nbsp;Ziwei Zhang,&nbsp;Sizhe Wang","doi":"10.1002/mma.70835","DOIUrl":"https://doi.org/10.1002/mma.70835","url":null,"abstract":"<div>\u0000 \u0000 <p>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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15552-15573"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite-Time Synchronization of Multi-Weighted Fractional-Order Complex Neural Networks","authors":"Muhammad Shakeel,&nbsp;Xinge Liu,&nbsp;Meilan Tang,&nbsp;Shuailei Zhang,&nbsp;Nadeem Khan","doi":"10.1002/mma.70847","DOIUrl":"https://doi.org/10.1002/mma.70847","url":null,"abstract":"<div>\u0000 \u0000 <p>This article explores the finite-time synchronization (FTS) of multi-weighted fractional-order complex neural networks (MWFOCNNs) with time-varying delays. By employing Lyapunov stability theory and fractional-order inequalities, several sufficient conditions are derived to ensure the FTS of multi-weighted fractional-order complex neural networks (MWFOCNNs) with time-varying delay. The proposed approach incorporates Lyapunov direct method and the Razumikhin condition to handle the time-varying delays. Finally, two numerical examples are presented to validate the effectiveness and accuracy of the proposed technique in achieving finite-time synchronization.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15778-15795"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Robust Analytical Framework for Solving Nonlinear Differential Equations Arising in Physical Sciences","authors":"Saurabh Tomar","doi":"10.1002/mma.70844","DOIUrl":"https://doi.org/10.1002/mma.70844","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we propose an effective analytical framework for solving nonlinear differential equations, termed the quasi-linearized Picard iteration method (QPIM). This method combines Newton's quasilinearization technique, which is known for its quadratic convergence, with the Picard iteration method, which offers a straightforward iterative framework. The proposed approach converts nonlinear differential equations into a sequence of linear problems via quasilinearization, which are then solved analytically using Picard iterations. A detailed convergence analysis confirms the quadratic rate of convergence under suitable conditions. Several examples are provided to illustrate the applicability and accuracy of the QPIM. Numerical comparisons revealed that QPIM achieved higher accuracy with fewer iterations. Furthermore, the QPIM provides monotonic sequences of approximations, enabling pointwise upper and lower bounds for solutions, which is especially useful for problems with unique solutions. These advantages establish the QPIM as a reliable tool for solving a broad class of nonlinear differential equations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15796-15821"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Iterations of Endomorphisms for 4-Torsion Subgroups of Elliptic Curve","authors":"Yutong Fan,&nbsp;Chi Young Ahn,&nbsp;Daeyeoul Kim","doi":"10.1002/mma.70836","DOIUrl":"https://doi.org/10.1002/mma.70836","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we consider sequences generated by iterated matrix multiplication, and introduce a classification of stable, amicable pair, and sociable matrix sequences. Based on these classifications, we analyze the behavior of subgroup sequences obtained through iterated endomorphism on the 4-torsion subgroups of elliptic curves. In addition, we present visual interpretations of these iterations, including symmetric patterns such as four-leaf clovers.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15696-15729"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Prüfer Angle Approach to Dependence of Eigenvalue for Sturm-Liouville Problem With Distributional Potentials","authors":"Gaofeng Du,&nbsp;Chenghua Gao","doi":"10.1002/mma.70787","DOIUrl":"https://doi.org/10.1002/mma.70787","url":null,"abstract":"<div>\u0000 \u0000 <p>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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14355-14362"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and Stability of Traveling Wavefronts in a Diffusive Vector Disease Model With Nonlocal Distributed Delay","authors":"Cun-Hua Zhang,&nbsp;Xiang-Ping Yan","doi":"10.1002/mma.70796","DOIUrl":"https://doi.org/10.1002/mma.70796","url":null,"abstract":"<div>\u0000 \u0000 <p>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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{R} $$</annotation>\u0000 </semantics></math>. 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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14486-14501"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of Random Diffusion and Advection on a Predator–Prey Model","authors":"Yu-Xia Wang,&nbsp;Peng-Xiang Zhang","doi":"10.1002/mma.70799","DOIUrl":"https://doi.org/10.1002/mma.70799","url":null,"abstract":"<div>\u0000 \u0000 <p>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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 13","pages":"14432-14456"},"PeriodicalIF":2.0,"publicationDate":"2026-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}