Mathematical Methods in the Applied Sciences最新文献

{"title":"The Head-Wave Ray Transform","authors":"Maarten V. de Hoop,&nbsp;Antti Kykkänen,&nbsp;Rohit Kumar Mishra","doi":"10.1002/mma.70846","DOIUrl":"https://doi.org/10.1002/mma.70846","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce and study a new integral ray transform called the head-wave transform. The head-wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths corresponds to ray paths of head-waves propagating in a medium with sharp changes in sound speed. The middle part of the ray paths corresponds to gliding along the so-called gliding surface. As our main results, we prove inversion formulas and null space characterizations under multiple different sets of assumptions on the geometry of the gliding surface and the integrand function.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15628-15646"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753481","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":"Averaging Principle for A Stochastic Delayed Avian Influenza Model with Impulsive Perturbations and Fractional Riemann-Liouville-Type Contact Rates","authors":"ShuangYan Yang,&nbsp;Kui Liu","doi":"10.1002/mma.70841","DOIUrl":"https://doi.org/10.1002/mma.70841","url":null,"abstract":"<div>\u0000 \u0000 <p>Upon exposure to infectious individuals, susceptible hosts exhibit heterogeneous clinical manifestations ranging from viral carriage without overt symptomatology to progressive symptomatic infection under the effects of the incubation period and external environmental disturbances. Meanwhile, the current rate of change in the number of susceptible hosts is influenced not only by ongoing contact with infected hosts during the incubation period, but also by previous interactions. To characterize the memory and historical cumulative effects of this infection process, this paper formulates a stochastic delayed avian influenza model with impulsive perturbations and fractional Riemann-Liouville-type contact rates. The well-posedness of mild solutions for this model is established using the semigroup method and the Banach fixed-point theorem. Additionally, an averaging principle is derived by employing inequality techniques and appropriate transformations for the fractional avian influenza model. The theoretical results indicate that the solution of the original impulsive avian influenza system can be effectively approximated by that of a simplified non-impulsive temporally averaged stochastic system, thereby providing a way to reduce system complexity. Numerical simulations are presented to validate the theoretical results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15647-15673"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753466","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":"Babenko's Method for \u0000 \u0000 \u0000 q\u0000 \u0000 $$ q $$\u0000 -Fractional Integral Equations: A Systematic Framework","authors":"Min-Jie Luo,&nbsp;Xue-Lin Zhou","doi":"10.1002/mma.70845","DOIUrl":"https://doi.org/10.1002/mma.70845","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we first introduce a generalized form of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-Mittag-Leffler function and use it as the integral kernel to construct a new type of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-fractional integral operators. We study the boundedness of these operators on the space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>a</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ {L}_q^pleft(0,aright) $$</annotation>\u0000 </semantics></math> and characterize their composition structures via discrete convolution for sequences. Subsequently, we apply Babenko's method (also known as the inverse operator method) to investigate the existence and uniqueness of solutions as well as the Hyers-Ulam stability for a class of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$$ q $$</annotation>\u0000 </semantics></math>-fractional integral equations involving such operators. Some illustrative examples and useful connections to other fields (especially fractional calculus based on Sonine kernels) are also discussed.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15674-15695"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753614","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 Class of Spectral Derivative-Free Projection-Based Methods with Inertial Strategy for Large-Scale Constraint Nonlinear System of Monotone Equations and Applications to Image Restoration Problems","authors":"Xiaoliang Wang","doi":"10.1002/mma.70840","DOIUrl":"https://doi.org/10.1002/mma.70840","url":null,"abstract":"<div>\u0000 \u0000 <p>Combining the derivative-free projection-based method, the spectral strategy and the inertial technique, in this paper, a class of inertial spectral three-term derivative-free projection-based methods are proposed for large-scale constraint nonlinear system of monotone equations. The proposed methods are suitable for large-scale problems without convexity and differentiability. Moreover, the sufficient descent property and the trust region property are satisfied independent of line search techniques. Meanwhile, the global convergence and the linearly convergent rate are established under standard conditions, respectively. 220 testing problems with feasible or infeasible initial points and the dimensions varying from 1000 to 100,000 are referred in the numerical experiment. Numerical results denote that the proposed methods are more effective and robust than the other derivative-free projection-based methods. Furthermore, the proposed methods are applied to some image restoration problems and the results also indicate that our methods are effective and promising.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15595-15627"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753444","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":"On the Eigenvalues of the Biharmonic Steklov Problem on a Thin Set","authors":"Bauyrzhan Derbissaly,&nbsp;Nurbek Kakharman","doi":"10.1002/mma.70850","DOIUrl":"https://doi.org/10.1002/mma.70850","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary conditions. The thin set is a tubular neighborhood &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;ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {omega}_{varepsilon } $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a planar smooth domain &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Omega $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We prove that, as &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ varepsilon to 0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, all Steklov eigenvalues satisfy &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;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∼&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {lambda}_{varepsilon, k}sim varepsilon {lambda}_k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &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;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {lambda}_k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ k $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;th eigenvalue of an explicit one-dimensional limiting problem on &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;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15822-15838"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148754209","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 HIV-1 Dynamic Model With Degenerate Diffusion, Time Delay and Immune Impairment","authors":"Li Yang,&nbsp;Yantao Luo,&nbsp;Tingting Zheng,&nbsp;Zhidong Teng","doi":"10.1002/mma.70842","DOIUrl":"https://doi.org/10.1002/mma.70842","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;Considering the coupled effects of multiple key biological mechanisms, including diffusion effects, the time delay in viral maturation and immune impairment, we innovatively propose a highly comprehensive reaction–diffusion dynamics model for HIV-1 infection. First, we analyze the well-posedness for the model, including the global existence, uniqueness, non-negativity, and boundedness of solutions. Second, we compute the immune-unactivated reproduction number &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;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and the immune-activated reproduction number &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;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. By employing Lyapunov functionals and LaSalle's invariance principle, we prove the global threshold dynamics of the model. Furthermore, we demonstrate that when &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;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0&lt;1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the system admits no traveling wave solutions connecting the infection-free equilibrium to itself. Finally, numerical simulations not only validate these theoretical results but also reveal that the virus-to-cell transmission route exhibits higher sensitivity in influencing &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;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {R}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, while reducing the immune impairment rate significantly enhances the intensity of the CTL response. This study provides a unified theoretical framework for understanding HIV-1 infection dynamics under complex biological factors and offers mathematical insights for optimizing combination therapeutic strategies.&lt;/p&gt;\u0000 &lt;","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15753-15777"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753706","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":"Hermite Wavelet Operational Matrix Method for Solving Neutral Coupled Delay Differential Equations With Multiple Delays","authors":"Saranya Krishnamoorthy,&nbsp;Swaminathan Ganesan,&nbsp;Hossein Jafari","doi":"10.1002/mma.70828","DOIUrl":"https://doi.org/10.1002/mma.70828","url":null,"abstract":"<div>\u0000 \u0000 <p>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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15534-15551"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753396","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":"New Exploration on Approximate Controllability of Nonlinear \u0000 \u0000 \u0000 Ψ\u0000 \u0000 $$ Psi $$\u0000 -Hilfer Fractional Neutral-Type Delayed Integro-Differential Stochastic Inclusions","authors":"Om Prakash Kumar Sharma,&nbsp;Ramesh Kumar Vats,&nbsp;Ankit Kumar","doi":"10.1002/mma.70837","DOIUrl":"https://doi.org/10.1002/mma.70837","url":null,"abstract":"<div>\u0000 \u0000 <p>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 <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ψ</mi>\u0000 </mrow>\u0000 <annotation>$$ Psi $$</annotation>\u0000 </semantics></math>-Hilfer fractional derivative has been considered, which has a quality to choose a suitable kernel function <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ψ</mi>\u0000 </mrow>\u0000 <annotation>$$ Psi $$</annotation>\u0000 </semantics></math>. First, by making use of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ψ</mi>\u0000 </mrow>\u0000 <annotation>$$ Psi $$</annotation>\u0000 </semantics></math>-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.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15495-15516"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753141","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":"Approximate Controllability Results for Stochastic Pantograph Integro-Differential Inclusions With Hilfer Fractional Substantial Derivative","authors":"Ayoub Louakar,&nbsp;Devaraj Vivek,&nbsp;Ahmed Kajouni,&nbsp;Khalid Hilal","doi":"10.1002/mma.70838","DOIUrl":"https://doi.org/10.1002/mma.70838","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper studies the existence and approximate controllability for a class of stochastic pantograph-type integro-differential inclusions with fractional Hilfer substantial derivative in Hilbert spaces. The existence of mild solutions is established using the Bohnenblust-Karlin fixed point theorem, in conjunction with techniques from fractional calculus, semi-group theory, measure of noncompactness, and stochastic analysis. The study of approximate controllability is conducted by presuming that the related linear system exhibits this property, which in turn facilitates the derivation of sufficient criteria for governing the nonlinear system. A specific example is given to demonstrate the effectiveness and practicality of the theoretical findings.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15574-15594"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753443","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":"Transition From Stability to Chaos in High Performance Fiber Materials Using Predictive Modeling","authors":"Ifrah Iqbal,&nbsp;Adil Jhangeer,&nbsp;Hamood Ur Rehman,&nbsp;Ghazala Akram,&nbsp;Yakup Yildirim","doi":"10.1002/mma.70848","DOIUrl":"https://doi.org/10.1002/mma.70848","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper offers a thorough analytical and numerical analysis of nonlinear dynamics under the Ablowitz-Kaup-Newell-Segur (AKNS) water wave equation, particularly in its possible applicability to advanced fiber materials. Utilizing an appropriate wave transformation, the governing nonlinear partial differential equation is simplified into an ordinary differential equation, which is solved exactly using the generalized Riccati equation mapping method (GREMM). The closed-form solutions form the basis for a systematic study of the system's rich dynamical features such as equilibrium states, bifurcations, multi-stability, and chaos. Bifurcation analysis identifies the key transitions, demonstrating the routes from stable periodic oscillations to irregular and chaotic states. Numerical simulations also confirm these transitions, demonstrating the system's evolution between regular, quasi-periodic, and fully developed chaotic states. Illustrations like phase portraits, temporal evolution of series, Lyapunov exponents, Poincaré sections, and recurrence plots attest to the existence of chaos, fractal-like self-similarity, and huge sensitivity to initial conditions. Multi-stability, which is the coexistence of more than one attractor under the same parameter conditions, highlights the tenuous balance of nonlinear responses in complex systems. These results are most directly applicable to high-performance fiber materials, in which wave propagation, stress-strain instabilities, and nonlinear dynamic responses have a profound impact on performance and reliability. The revealed bifurcation and chaos mechanisms shed light on how fiber composites, smart fibers, and adaptive materials could switch between different mechanical states under different loads, impacts, or environmental inputs. Mapping the entire bifurcation topology of the system provides a predictive platform for designing fibers with improved vibration damping, impact resistance, and energy absorption properties. In general, this work demonstrates the strength of linking analytical exact solutions with numerical computations in revealing the subtle interaction among nonlinearity, parameter variation, and dynamic behavior, providing insightful viewpoints toward designing and controlling next-generation fiber materials and fiber-reinforced structures. The novelty of this work lies in the integration of exact analytical solutions with advanced chaos diagnostics, providing deeper insight into the interplay between nonlinearity and system dynamics, and extending beyond existing studies by offering both a broader solution spectrum and a comprehensive dynamical characterization.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"49 14","pages":"15899-15927"},"PeriodicalIF":2.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148753719","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}