Mathematical Methods in the Applied Sciences最新文献

{"title":"Well-Posedness of a Semilinear Fractional Diffusion Equation With Caputo Derivative and Special Boundary Conditions","authors":"Zakaria Hamdi,&nbsp;Lamine Bouzettouta","doi":"10.1002/mma.70744","DOIUrl":"https://doi.org/10.1002/mma.70744","url":null,"abstract":"<div>\u0000 \u0000 <p>We study a semilinear time-fractional diffusion equation in one spatial dimension, where the time derivative is understood in the sense of Caputo. The problem is complemented with suitable boundary conditions, possibly of moving type. We establish the existence, uniqueness, and regularity of weak solutions under natural assumptions on the data and nonlinearities. The analysis relies on fractional calculus tools, including estimates for the Mittag–Leffler function and a fractional Grönwall inequality. Extensions to nonlinear boundary conditions and moving interfaces are also discussed.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13201-13215"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148576136","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 Novel Optimized Local Linearization Hybrid Block Method for Chaotic Systems: Applications to Stretch-Twist-Fold Flow and Bond Orbital Chaotic Attractors","authors":"Shina Daniel Oloniiju,&nbsp;Anastacia Dlamini","doi":"10.1002/mma.70731","DOIUrl":"https://doi.org/10.1002/mma.70731","url":null,"abstract":"<p>The numerical approximation of nonlinear chaotic differential systems, such as the modified stretch-twist-fold (STF) flow and multi-bond chaotic attractors, presents a significant challenge due to their sensitive dependence on initial conditions and complex dynamics where analytical solutions are unattainable. While many numerical techniques exist, they often struggle to simultaneously achieve the high accuracy, absolute stability and computational efficiency required to reliably capture these intricate behaviors. To address this gap, this study introduces and validates an optimized local linearization hybrid block method (LLHBM). The proposed method uniquely combines Newton-Raphson and Gauss-Siedel-type linearization techniques within a robust framework of the hybrid block methods, integrating linear multistep methods with interpolation and collocation. A key optimization involves selecting the intra-step points as the normalized extrema of Legendre polynomials, which demonstrably enhances both the accuracy and stability of the numerical scheme. Theoretical analysis confirms that the LLHBM is absolutely stable and achieves a high-order truncation error of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$$ M+2 $$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 </mrow>\u0000 <annotation>$$ M $$</annotation>\u0000 </semantics></math> is the number of intra-step points. Through detailed numerical experiments, including analyses of residual and convergence error norms, the study validates the robustness, efficiency and precision of the numerical method in capturing the complex dynamics of the chaotic systems. These results establish the LLHBM as a reliable tool for solving nonlinear chaotic differential equations, offering superior computational efficiency and stability compared to other traditional numerical methods.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13148-13175"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70731","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148576135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Investment-Reinsurance Design Under Asymmetric Nash Bargaining in a Square Root Factor Process for Jump-Diffusion Risk Model","authors":"Fengzhu Chang,&nbsp;Jia Yao,&nbsp;Junna Bi","doi":"10.1002/mma.70743","DOIUrl":"https://doi.org/10.1002/mma.70743","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies an investment-reinsurance contract between an insurer and a reinsurer with asymmetric bargaining power. We assume that the surplus of the insurer follows a jump-diffusion process. To reduce the risk of claims, the insurer can purchase proportional reinsurance, with the reinsurance premium calculated based on the expected value principle. The surplus of the insurer and the reinsurer can be allocated to a financial market consisting of a risk-free asset and a risky asset, respectively. The price processes of the insurer's and reinsurer's risky assets satisfy different square root factor processes. To consider the benefits of both the insurer and the reinsurer, the optimization problem is formulated as an asymmetric Nash bargaining game. To maximize the weighted product of the expected exponential utility of the terminal wealth of both parties, explicit expressions for the Pareto-optimal strategy and the corresponding value function are derived by employing stochastic control techniques and the Hamilton-Jacobi-Bellman (HJB) equation. In addition, we provide equilibrium strategies under several special cases, including cases where only the insurer or the reinsurer is considered, as well as models under the CEV (Constant Elasticity of Variance) model and the Heston stochastic volatility model. Finally, numerical examples illustrate the impact of bargaining power on optimal strategy.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13247-13266"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148576138","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":"Optimal Control and Cost-Effectiveness of Vaccination and Treatment for Cholera-Hepatitis E Co-Infection","authors":"Paul Chataa,&nbsp;Samuel M. Naandam,&nbsp;Bismark Oduro,&nbsp;Fred Ameko","doi":"10.1002/mma.70738","DOIUrl":"https://doi.org/10.1002/mma.70738","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Observational evidence confirms the essential role of vaccination and treatment in reducing and potentially eliminating cholera and hepatitis E virus (HEV) infections. Mathematical modeling is a powerful tool for identifying effective strategies to control disease transmission. This study develops a detailed mathematical model to describe the dynamics of cholera-HEV co-infection, incorporating vaccination and treatment as time-dependent control measures. To ensure the model's validity, key mathematical properties such as positivity and boundedness are examined, confirming that the system is well-posed. The control reproduction number &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left({mathcal{R}}_cright) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is calculated using the next-generation matrix method, and both disease-free and endemic equilibria are analyzed. Results show that the disease-free equilibrium is locally and globally asymptotically stable, while the boundary endemic equilibria also exhibit global stability. Sensitivity analysis using latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) identifies parameters that most influence &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℛ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathcal{R}}_c $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The model is extended to simulate dynamic intervention strategies, including vaccination and treatment. Numerical simulations support the analytical results, demonstrating how these strategies reduce infection rates in both singly and co-infected populations. Simulations without treatment show an initial rise in infection levels, followed by a gradual decline. This highlights the importance of therapeutic measures, though their effectiveness may be limited by issues such as drug resistance and limited vaccine access. These findings emphasize the need for integrated intervention strategies, especially in light of reinfection cases reported in the literature. Finally, cost-effectiveness analysis shows that treatment-only strategies offer the highest economic efficiency, making them the most favorable option among the interventions evaluated. These insights can help policymakers make balanced, practical decisions when adjusting preventive measures for cholera and HEV control.&lt;/p&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"13284-13323"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148576141","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":"Unbounded Generalization of the Baker–Campbell–Hausdorff Formulae","authors":"Yoritaka Iwata","doi":"10.1002/mma.70677","DOIUrl":"https://doi.org/10.1002/mma.70677","url":null,"abstract":"<div>\u0000 \u0000 <p>Based on the operator representation on the module over a Banach algebra, the Baker–Campbell–Hausdorff formula is generalized to be applicable to unbounded infinitesimal generators in Banach spaces. For this purpose, it is necessary to extract a bounded component from a given generally unbounded infinitesimal generator. In this paper, much attention is paid to clarifying the unknown relation between the commutator product and the logarithm of operators. In conclusion, by means of the logarithmic representation of generally unbounded operators, the Baker–Campbell–Hausdorff formula is generalized. As an application, a logarithmic form of the von Neumann equation is presented in which the role of the logarithm as the commutator is clearly seen.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 12","pages":"12989-13000"},"PeriodicalIF":2.0,"publicationDate":"2026-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148565142","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":"Sherman–Morrison–Woodbury Formula-Based Efficient Preconditioners for Sequences of Shifted Linear Systems","authors":"Bing-Qian Zhao,&nbsp;Jia-Lin Zhang,&nbsp;Li-Hua Wei,&nbsp;Li-Dan Liao","doi":"10.1002/mma.70578","DOIUrl":"https://doi.org/10.1002/mma.70578","url":null,"abstract":"<div>\u0000 \u0000 <p>This study explores iterative methods for solving sequences of shifted linear systems expressed as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>A</mi>\u0000 <mo>+</mo>\u0000 <mi>α</mi>\u0000 <mi>I</mi>\u0000 <mo>)</mo>\u0000 <mi>x</mi>\u0000 <mo>=</mo>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 <annotation>$$ left(A+alpha Iright)x=b $$</annotation>\u0000 </semantics></math>. To address these systems efficiently, we utilize the preconditioned generalized minimum residual (PGMRES) method, enhanced by a tailored preconditioning strategy. Our approach combines the Sherman-Morrison-Woodbury (SMW) formula with selective dropping techniques to optimize performance. The preconditioners are constructed through an incomplete factorization of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {A}^{-1} $$</annotation>\u0000 </semantics></math>, leveraging a biconjugate gradient algorithm. Our results show that the eigenvalues of the preconditioned matrices exhibit tighter clustering around unity compared to those generated by conventional preconditioners. We also provide a rigorous convergence analysis for the iterative process. Finally, numerical experiments validate the effectiveness of our proposed method.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 11","pages":"11643-11660"},"PeriodicalIF":2.0,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148373409","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":"Chaos and Complexity in a Novel Three-Dimensional Nonlinear System: Analysis, Bifurcations, and Applications","authors":"Faruk Biswas,&nbsp;Santosh Biswas,&nbsp;Raihan Islam Mondal,&nbsp;Sujay Goldar,&nbsp;Sk. Sarif Hassan,&nbsp;Purnendu Sardar","doi":"10.1002/mma.70660","DOIUrl":"https://doi.org/10.1002/mma.70660","url":null,"abstract":"<div>\u0000 \u0000 <p>This study introduces a novel three-dimensional nonlinear system featuring quadratic, cubic, quartic, and quintic nonlinearities, with inherent symmetry about the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>z</mi>\u0000 </mrow>\u0000 <annotation>$$ z $$</annotation>\u0000 </semantics></math>-axis. We analyze its fundamental dynamical properties, including equilibrium points and their stability, dissipative behavior, and high-periodicity limit cycles. The system's chaotic nature is rigorously examined through Lyapunov exponent spectra, fractal dimension analysis, and Poincaré maps, revealing sensitivity to initial conditions and parameter variations. A detailed bifurcation analysis identifies critical transitions, including Hopf bifurcations, using both numerical simulations and theoretical criteria such as the Routh-Hurwitz stability conditions. Notably, the system exhibits rich dynamics, from stable equilibria to chaotic attractors, with fractional Lyapunov dimensions confirming its complexity. Practical implications are underscored by parameter ranges yielding chaotic trajectories, validated through circuit-compatible amplitude constraints. The system's versatility suggests promising applications in cryptography, secure communications, and random number generation, motivating further exploration of its nonlinear phenomena.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 11","pages":"11594-11618"},"PeriodicalIF":2.0,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148373106","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":"Dynamics of Soliton Solutions, Dynamical Transitions, and Statistical Features of Noise-Induced Multistable Nonlinear Systems","authors":"Maham Munawar,&nbsp;Adil Jhangeer","doi":"10.1002/mma.70651","DOIUrl":"https://doi.org/10.1002/mma.70651","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we will give a comprehensive theoretical and computational discussion of the concept of the fractional nonlinear dispersive systems, and how deterministic and stochastic driving forces influence complex oscillatory dynamics. Special attention is given to the overlap of soliton solutions which throws light on the sensitivity and stability of nonlinear waveforms that are of importance in plasma physics and optics. Despite bifurcation structures indicating ways to chaos and simultaneous multi-stable states, dynamical geometry in analyzing bifurcation structures has shown fractal basin geometries, multistability transitions and attractor sensitivity. Periodically forced and noise-driven oscillators are compared and an analysis of methods of controlling chaos, including OGY-based stabilization, are also analyzed. Statistical indicators of stability, the coherence, and attractor geometry are measured in both deterministic and stochastic regimes by the methods of spectral analysis, complexity based on entropy, stochastic synchronization, and Monte Carlo simulation. When combined, these analyzes provide a cohesive method for identifying multistability, assessing basin resilience, and achieving efficient control in a system with nonlinear oscillations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 11","pages":"11562-11593"},"PeriodicalIF":2.0,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148373105","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":"Persistence of Traveling Wave Solutions of the Perturbed Klein-Gordon-Zakharov Equations","authors":"Yuheng Jiang,&nbsp;Yu Tian,&nbsp;Yao Qi","doi":"10.1002/mma.70590","DOIUrl":"https://doi.org/10.1002/mma.70590","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is concerned with the persistence of solitary wave solutions and periodic wave solutions of the perturbed Klein-Gordon-Zakharov equations (KGZEs). Combining geometric singular perturbation (GSP) theory, Melnikov methods, invariant manifold theory, and bifurcation theory, we prove that solitary wave solutions and periodic solutions of the KGZEs still persist under small perturbation when the specific wave velocity is selected. Additionally, we prove that the periodic orbits lead to the emergence of a hyperbolic limit cycle near the original periodic orbit when perturbed, and that other periodic orbits in the small neighborhood of the original periodic orbit break apart and tend to approach this hyperbolic limit cycle.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 11","pages":"11763-11774"},"PeriodicalIF":2.0,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148373196","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":"Computing Bonds Between Formal Contexts","authors":"Roberto G. Aragón,&nbsp;Jesús Medina,&nbsp;Samuel Molina-Ruiz","doi":"10.1002/mma.70597","DOIUrl":"https://doi.org/10.1002/mma.70597","url":null,"abstract":"<p>The notion of bond was introduced as a technique to aggregate information from multiple datasets without modifying the information already present in each of the datasets. This notion has been extended to several fuzzy frameworks, including the residuated lattice setting, which we also consider in this paper. While most studies on bonds have emphasized their role in aggregating contexts, relatively little attention has been given to how they can be effectively computed. In this paper, we address this gap by introducing algorithms to compute all bonds between two contexts in both the classical and residuated lattice setting.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 11","pages":"11661-11677"},"PeriodicalIF":2.0,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70597","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148373319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}