Mathematical Methods in the Applied Sciences最新文献

{"title":"Intraguild Predation and Competitions of Two Stage-Structured Species in a Seasonal Patchy Model","authors":"Feng-Bin Wang,&nbsp;Chang-Yuan Cheng","doi":"10.1002/mma.10813","DOIUrl":"https://doi.org/10.1002/mma.10813","url":null,"abstract":"<div>\u0000 \u0000 <p>Some creatures interact with not only the same species but also different species by competing resources and even develop intraguild predation (IGP) to improve their survival. Individuals also react for survival according to spatial heterogeneity and seasonal variation of the environment. However, all these creatures' behaviors may change in their different life stages because of varied physiological structures. Considering these concerns, we propose a two-patch model with environmental seasonality and individuals' two life stages and incorporate intraspecific and interspecific competitions and IGP between two species. We begin by analyzing single-species models to establish threshold dynamics. This analysis shows that a species will eventually go extinct or exhibit oscillatory population dynamics across both patches, attracting all nonnegative solutions. Next, we explore two-species models, without and with IGP, and formulate the invasion indices for both species in each scenario. In both cases, we demonstrate that the population tends to die out if the invasion indices are less than one while remaining persistent if the invasion indices exceed one. Finally, we conduct numerical examples to verify the criterion for threshold dynamics and observe some interesting results, including IGP can reverse the competition outcome, IGP can induce ecological diversity, seasonality can facilitate species survival, and prey species can adapt their maturation time against IGP.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 9","pages":"9490-9507"},"PeriodicalIF":2.1,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143950321","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":"General Decay and Blowing-Up Solutions of a Nonlinear Wave Equation With Nonlocal in Time Damping and Infinite Memory","authors":"Mokhtar Kirane,&nbsp;Radhouane Aounallah,&nbsp;Lotfi Jlali","doi":"10.1002/mma.10777","DOIUrl":"https://doi.org/10.1002/mma.10777","url":null,"abstract":"<p>This paper shows that long-term stability and blowing-up solutions for a nonlinear wave equation with a nonlocal damping of Choi and MacCamy type and a nonlocal dispersion can occur. The method of proof of general decay relies on a suitable Lyapunov functional. The method of proof of blow up in finite time of some solutions relies on the concavity method.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9046-9057"},"PeriodicalIF":2.1,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10777","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909378","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":"Infinitely Many Solutions for Singular \u0000p(x)-Laplacian Equation Without the Ambrosetti–Rabinowitz (AR) Condition","authors":"D. Choudhuri,&nbsp;K. Saoudi","doi":"10.1002/mma.10760","DOIUrl":"https://doi.org/10.1002/mma.10760","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We establish the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation with singularity: \u0000\u0000 &lt;/p&gt;&lt;div&gt;&lt;span&gt;&lt;!--FIGURE--&gt;\u0000 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtable&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mtd&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mtext&gt;in&lt;/mtext&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"8870-8883"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909657","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 a Generalized Superellipse: From Models to Applications","authors":"Ivana Kovacic","doi":"10.1002/mma.10795","DOIUrl":"https://doi.org/10.1002/mma.10795","url":null,"abstract":"<div>\u0000 \u0000 <p>This study is concerned with a power-form functional equation and its various forms in Cartesian and polar coordinates. An overview of the related contributions is presented and illustrated in terms of the shapes that they can yield, thereby establishing cross-disciplinary phenomenological links by demonstrating the application of identical mathematical models across diverse fields within nonlinear science, marking a novel approach in this context. Finally, an analytical solution of this equation is elaborated both with respect to its form as a functional equation and as a Hamiltonian function. The original solutions in terms of trigonometric or generalized trigonometric functions are presented as well.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9344-9349"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909663","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":"Application of De La Vallée Poussin Type Inequalities to Half-Linear Euler Type Equations","authors":"Zuzana Pátíková","doi":"10.1002/mma.10802","DOIUrl":"https://doi.org/10.1002/mma.10802","url":null,"abstract":"<p>The paper is devoted to the application of de la Vallée Poussin type inequalities to half-linear differential Euler type equations. Four studied equations seen as perturbations of the nonoscillatory Euler equation with the oscillation constant are considered, and a new theorem for the cases where the perturbation is in both terms is presented. Several different corollaries of de la Vallée Poussin type inequalities for Euler type equations, which can help in estimating the distance between consecutive zero points of their solutions, are formulated.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9332-9339"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10802","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909320","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":"Localized Wave and Other Special Wave Solutions to the (3 + 1)-dimensional Kudryashov–Sinelshchikov Equation","authors":"Kang-Jia Wang,&nbsp;Shuai Li,&nbsp;Guo-Dong Wang,&nbsp;Peng Xu,&nbsp;Feng Shi,&nbsp;Xiao-Lian Liu","doi":"10.1002/mma.10764","DOIUrl":"https://doi.org/10.1002/mma.10764","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper aims to explore some different localized wave solutions to the (3 + 1)-dimensional Kudryashov–Sinelshchikov equation (KSe) for the liquid with gas bubbles. First, the traveling wave transformation is employed to reduce the dimension of the (3 + 1)-dimensional KSe. Then the Hirota bilinear method is adopted to develop the rogue wave solutions via introducing the different polynomial functions. By optimizing the parameters, the bright and dark rogue waves solutions of the first-order and second-order are extracted. In addition, the three-wave method is employed to seek the generalized breathers wave, <i>W</i>-shape (double well or breather wave), bright and dark solitary wave solutions. Besides, the other special wave solutions like the compacton and singular wave solutions are also reported. Meanwhile, the dynamic attributes of some solutions are unfolded by Maple. To the best of the authors' knowledge, the findings of this research are all new and have not explored in other literature.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"8911-8924"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909656","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":"Dynamic Properties of a Prey–Predator Food Chain Chemostat Model With Ornstein–Uhlenbeck Process","authors":"Xiao Chen,&nbsp;Miaomiao Gao,&nbsp;Yanhui Jiang,&nbsp;Daqing Jiang","doi":"10.1002/mma.10797","DOIUrl":"https://doi.org/10.1002/mma.10797","url":null,"abstract":"<div>\u0000 \u0000 <p>The food chain in an ecosystem is a complex, interconnected system of organisms that depend on each other and their environment. Chemostat model can be used to evaluate the stability and resilience of the food chain, as well as the response capacity of the system in the face of different disturbances and environmental changes. In this paper, we construct a prey–predator food chain chemostat model with Ornstein–Uhlenbeck processes and consider the dynamics of this stochastic model. Firstly, we prove the existence and uniqueness of the global solution. Secondly, we deduce the extinction in two cases: One is the extinction of prey and predator, and the other is the extinction of predator and the survival of prey. In addition, by constructing appropriate Lyapunov functions, we obtain the sufficient condition for the existence of stationary distribution, which means that prey and predator can coexist over a long period of time. Then, on this basis, we give the concrete expression of the density function of the distribution around the positive equilibrium point of corresponding deterministic system. Finally, numerical simulations prove the correctness of the theoretical results and show how the speed of reversion and intensity of volatility affect the food chain behavior.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9253-9271"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909661","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 Strong Approximation in \u0000L2 for the Solutions of the Maxwell System With Highly Oscillating Periodic Coefficients","authors":"Juan Casado-Díaz,&nbsp;Nourelhouda Khedhiri,&nbsp;Mohamed Lazhar Tayeb","doi":"10.1002/mma.10793","DOIUrl":"https://doi.org/10.1002/mma.10793","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;We consider a Maxwell system on \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&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;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {mathbb{R}}&amp;#x0005E;3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with highly oscillating periodic coefficients. It is known that the solutions converge in the weak-\u0000&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;/mrow&gt;\u0000 &lt;annotation&gt;$$ ast $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; topology of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&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;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&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;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {L}&amp;#x0005E;{infty}left(0,T;kern0.3em {L}&amp;#x0005E;2left({mathbb{R}}&amp;#x0005E;3right)right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to the solution of a similar problem with constant coefficients given as the \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ H $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-limits of the electric permittivity and the magnetic permeability, respectively, that is, the limit in the sense of the homogenization of linear elliptic equations with varying coefficients. However, it is not true that the elliptic corrector also provides a corrector for the solution of the Maxwell system, that is, an approximation of the solutions in the strong topology of \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9207-9224"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909662","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":"Exact Controllability for the Quasilinear Perturbations of the Kawahara Equation","authors":"Yanpeng Jin,&nbsp;Ying Fu,&nbsp;Xiaoping Wu","doi":"10.1002/mma.10789","DOIUrl":"https://doi.org/10.1002/mma.10789","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is devoted to studying the exact controllability for the Kawahara equation under the influence of quasilinear perturbations for sufficiently small data on the circle with localized control, the nonlinearities containing up to five space derivatives and having a Hamiltonian structure at the space derivatives of the highest order. Firstly, we conjugate the associated linearized operator to a time-dependent variable coefficient operator up to a bounded remainder. The major difficulties come from five space derivatives and the coupling of the coefficient of the highest order term with the coefficients of other terms. The strategy adopted is to look for appropriate transformations, which are reversible and satisfy the sharp bounds for the reducibility. Then, from the observability and controllability of the corresponding linear control problem, the existence of the right inverse for the linearized operator is verified. Finally, the application of the Nash–Moser–Hörmander theorem implies the exact controllability for the Kawahara equation with the quasilinear perturbations.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9160-9176"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909660","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":"The Truncated Euler–Maruyama Method for Caputo Fractional Stochastic Differential Equations","authors":"Jiajun Liu,&nbsp;Qiu Zhong,&nbsp;JianFei Huang","doi":"10.1002/mma.10801","DOIUrl":"https://doi.org/10.1002/mma.10801","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we firstly construct the truncated Euler–Maruyama (EM) method for Caputo fractional stochastic differential equations (Caputo FSDEs) with the local Lipschitz condition and the Khasminskii-type condition on drift and diffusion functions. After that, the boundedness and strong convergence of the numerical solutions are theoretically analyzed. Moreover, the strong convergence order of this presented truncated EM method is proved as \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>−</mo>\u0000 <mn>0</mn>\u0000 <mo>.</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <annotation>$$ alpha -0.5 $$</annotation>\u0000 </semantics></math>, where \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 <annotation>$$ alpha $$</annotation>\u0000 </semantics></math> denotes the order of Caputo derivative and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>.</mo>\u0000 <mn>5</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>α</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$$ 0.5&amp;lt;alpha &amp;lt;1 $$</annotation>\u0000 </semantics></math>. In the end, numerical experiments are demonstrated to confirm the correctness of the theoretical results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9320-9331"},"PeriodicalIF":2.1,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143909664","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}