Mathematical Methods in the Applied Sciences最新文献

{"title":"On the Solitons, Shocks, and Periodic Wave Solutions to the Fractional Quintic Benney–Lin Equation for Liquid Film Dynamics","authors":"Haifa A. Alyousef, Rasool Shah, Alvaro H. Salas, C. G. L. Tiofack, Sherif M. E. Ismaeel, Weaam Alhejaili, Samir A. El-Tantawy","doi":"10.1002/mma.10661","DOIUrl":"https://doi.org/10.1002/mma.10661","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, two improved versions related to the family of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mo>˜</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$$ tilde{G} $$</annotation>\u0000 </semantics></math>-approaches \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mtext>for simplicity, we will use from now on</mtext>\u0000 <mspace></mspace>\u0000 <mover>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mo>˜</mo>\u0000 </mover>\u0000 <mo>≡</mo>\u0000 <mfenced>\u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <msup>\u0000 <mrow></mrow>\u0000 <mrow>\u0000 <mo>′</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mfrac>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$$ left(mathrm{for} mathrm{simplicity},mathrm{we} mathrm{will} mathrm{use} mathrm{from} mathrm{now} mathrm{on}kern0.3em tilde{G}equiv left(frac{G^{prime }}{G}right)right) $$</annotation>\u0000 </semantics></math>, namely, the simple \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mo>˜</mo>\u0000 </mover>\u0000 </mrow>\u0000 <annotation>$$ tilde{G} $$</annotation>\u0000 </semantics></math>-expansion method and the generalized \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>r</mi>\u0000 <mo>+</mo>\u0000 <mover>\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6145-6164"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595084","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 Dynamical Behaviors of a Stochastic Mumps Infectious Disease Model","authors":"Suping Zhang,&nbsp;Feng Yang,&nbsp;Xiuyang Wu","doi":"10.1002/mma.10660","DOIUrl":"https://doi.org/10.1002/mma.10660","url":null,"abstract":"<div>\u0000 \u0000 <p>The study of infectious disease dynamics plays an important role in reflecting the transmission mechanisms of epidemics. Compared with the traditional statistical methods, understanding dynamics of an infectious disease can better make people understand some global characteristics of epidemic and help in designing appropriate strategies to control diseases. Early studies of mumps mainly focused on deterministic models. However, environmental noises are inevitable during the spread of infectious diseases. This paper extends a mumps transmission model from a deterministic to a stochastic framework and explores the dynamical behaviors of the model by constructing suitable Lyapunov functions. Our model is a six-dimensional stochastic model. The construction of suitable Lyapunov functions is very challenging. Firstly, we show that this model has a unique global positive solution for any positive initial values. Secondly, we compute the basic reproduction numbers and present sufficient conditions for the existence of a unique ergodic stationary distribution and the extinction of the disease. Finally, we perform numerical simulations and sensitivity analysis for exploring the effect of some parameters and the white noises on the behavior of the model. The theoretical results can provide necessary guidelines to public health administrators for controlling and preventing diseases.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6131-6144"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595020","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":"Complex Dynamics of a Memory-Induced Stage-Structured Diffusive System With Maturation Delay and Strong Allee Effect","authors":"Luhong Ye,&nbsp;Hongyong Zhao,&nbsp;Xuebing Zhang,&nbsp;Daiyong Wu","doi":"10.1002/mma.10664","DOIUrl":"https://doi.org/10.1002/mma.10664","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, a memory-induced stage-structured prey–predator diffusive system with maturation delay and strong Allee effect is proposed. First, the positivity of solutions and survival of the non-spatial system are studied. The results indicate that strong Allee effect affects the coexistence of two populations to maintain the harmonious development of the ecosystem, and they can coexist if and only if the predator's fertility is greater than its mortality when the prey reaches its peak. The non-spatial system can undergo Hopf bifurcation caused by the maturation delay. Then we obtain complex dynamics for the spatial system with spatial memory. On one hand, spatial memory diffusion and memory delay can bring about not only Hopf bifurcation and Turing bifurcation but also Turing-Hopf bifurcation and Bogdanov-Takens bifurcation with strong Allee effect. On the other hand, spatial memory delay and maturation delay could induce double Hopf bifurcation. Furthermore, we also investigate the global continuation of local periodic solutions for the spatial system without spatial memory. These interesting results may provide new clues for the investigation of the coexistence for the populations and understanding the complex dynamics of prey–predator systems.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6191-6207"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595019","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 and Synchronization of Complex-Valued Differential-Algebraic Neural Networks With Delay: A Differential-Algebraic Inequality Approach","authors":"Weiqiang Gong,&nbsp;Yao Xiao,&nbsp;Kai Wang,&nbsp;Qiang Li","doi":"10.1002/mma.10677","DOIUrl":"https://doi.org/10.1002/mma.10677","url":null,"abstract":"<div>\u0000 \u0000 <p>This article proposes a novel complex-valued differential-algebraic neural network model with time delay (DDANN). Firstly, based on the differential-algebraic inequality technique, the global stability criteria of the considered system are obtained to ensure the complex-valued DDANN achieves global exponential stability. Next, by designing an appropriate feedback controller, to get the desired results, we present some constraint conditions, which make the drive system and the response system achieve the global exponential synchronization. Furthermore, as an application, a complex-valued neutral-type neural network (NDNN) can be transformed into a simple complex-valued DDANN and the global exponential stability results of NDNN are also proposed. In the end of paper, two examples are given to verify the superiority/feasibility of the presented theoretical results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6361-6374"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622366","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":"Fast Crank-Nicolson Block-Centered Difference Scheme for a Tempered Time-Fractional Mobile/Immobile Equation With Variable Coefficients","authors":"Yuexiu Dong,&nbsp;Lijuan Nong,&nbsp;An Chen","doi":"10.1002/mma.10701","DOIUrl":"https://doi.org/10.1002/mma.10701","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we are interest in developing efficient numerical scheme for solving a two-dimensional tempered time-fractional mobile/immobile equation with time-space dependent coefficients, which arises in the modeling of groundwater flow and pollutant transport. By applying the fast modified L1 formula in time and the block-centered difference method in space, we establish a fully discrete fast Crank-Nicolson difference scheme. The stability and error estimate of the proposed scheme are strictly proved. To handle the initial weakly singularity of the solution, we also consider a fast nonuniform modified L1 formula to solve the model problem. The numerical tests, both smooth and nonsmooth solution cases, are demonstrated to verify the accuracy and efficiency of our scheme.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6634-6646"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622364","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 Optimal Controls for Generalized Riemann–Liouville Fractional Sobolev-Type Stochastic Integrodifferential Equations of Order \u0000ϑ∈(1,2)","authors":"M. Johnson,&nbsp;V. Vijayakumar,&nbsp;Kiwoon Kwon","doi":"10.1002/mma.10662","DOIUrl":"https://doi.org/10.1002/mma.10662","url":null,"abstract":"<div>\u0000 \u0000 <p>This manuscript addresses the optimal control of generalized Riemann–Liouville fractional (Hilfer fractional) Sobolev-type stochastic differential equations of order \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ϑ</mi>\u0000 <mo>∈</mo>\u0000 <mspace></mspace>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ vartheta in kern0.3em left(1,2right) $$</annotation>\u0000 </semantics></math> in separable Hilbert spaces. First, the existence of mild solutions for the system is established using the cosine family of operators and the Leray–Schauder fixed point theorem. Then, the existence of optimal control is demonstrated through Balder's theorem. Finally, an example is provided to illustrate the results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6165-6179"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595021","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":"Initial Boundary Value Problem for Partial Differential–Algebraic Equations With Parameter","authors":"Anar T. Assanova","doi":"10.1002/mma.10663","DOIUrl":"https://doi.org/10.1002/mma.10663","url":null,"abstract":"<div>\u0000 \u0000 <p>The paper addresses an initial boundary value problem for a partial differential–algebraic equation involving a parameter. An integral condition with respect to the time derivative of the unknown function is provided as an additional condition to determine this parameter. The Dzhumabaev parameterization method is employed to solve the problem. The domain is subdivided, and functional parameters are defined as the values of the solution along the internal lines of the subdomains. This reformulates the original problem into an equivalent initial boundary value problem for a system of hyperbolic equations with parameters and associated functional relations. The paper develops algorithms to solve the problem, demonstrating their applicability. Furthermore, conditions for the existence and uniqueness of a solution to the initial boundary value problem, involving the partial differential–algebraic equation with a parameter and discrete memory, are established.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6180-6190"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595018","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":"Construction of Solutions in a Broad Sense of Systems of First-Order Partial Differential Equations With Periodic Conditions","authors":"Altynshash Bekbauova,&nbsp;Akylbek Meirambekuly","doi":"10.1002/mma.10688","DOIUrl":"https://doi.org/10.1002/mma.10688","url":null,"abstract":"<div>\u0000 \u0000 <p>The work considers the existence and uniqueness of a solution in the broad sense of systems of differential equations with the same principal part and periodic conditions. Characteristic vector is constructed - functions of the system under study, solutions are defined in a broad sense. A matrix corresponding to a homogeneous system was constructed. Sufficient conditions for the existence and uniqueness of the solution in the broad sense of systems of partial differential equations with periodic conditions are obtained.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6506-6511"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622493","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 Analysis of a Delayed HIV Model With Latent Reservoir and Both Viral and Cellular Infections","authors":"Lili Lv,&nbsp;Junxian Yang,&nbsp;Zihao Hu,&nbsp;Dongmei Fan","doi":"10.1002/mma.10655","DOIUrl":"https://doi.org/10.1002/mma.10655","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper presents an HIV model with latent reservoir and a constant production rate of cytotoxic T lymphocytes (CTLs). The system incorporates two delays, intracellular delay \u0000&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;τ&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;$$ {tau}_1 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and immune response delay \u0000&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;τ&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;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {tau}_2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and considers two mechanisms of viral transmission in vivo: cell-to-cell and virus-to-cell. Based on the initial condition, a key threshold in the model, namely, the basic reproduction number \u0000&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; is obtained. Our focus is to investigate the impact of saturated immune delay on viral infection when CTLs are introduced at a constant rate. By constructing Lyapunov functionals, the stability conditions of equilibrium \u0000&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;E&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;$$ {E}_0 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and equilibrium \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;E&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;τ&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;/msub&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;/mrow&gt;\u0000 &lt;annotati","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6063-6080"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595665","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":"Null Controllability of Stochastic Degenerate Parabolic Equation With Convection Term","authors":"Lin Yan,&nbsp;Bin Wu","doi":"10.1002/mma.10686","DOIUrl":"https://doi.org/10.1002/mma.10686","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper concerns the null controllability of stochastic degenerate parabolic equation with convection term in weakly degenerate case. Due to the degeneracy, we first transfer to study an approximate nondegenerate system. Next, we establish the Carleman estimate for backward stochastic degenerate parabolic equation with convection term. In order to deal with the convection term, the Carleman estimate is established by introducing an auxiliary function to transfer the diffusion and the convection term into a whole complex divergence-like form. By this Carleman estimate, we then obtain an observability inequality for the adjoint system of the approximate system. Based on the observability inequality and an approximate argument, we proved our null controllability result.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6495-6505"},"PeriodicalIF":2.1,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622715","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}