{"title":"Application of the LDG method using generalized alternating numerical flux to the fourth-order time-fractional sub-diffusion model","authors":"Xindong Zhang , Leilei Wei , Juan Liu","doi":"10.1016/j.aml.2025.109580","DOIUrl":"10.1016/j.aml.2025.109580","url":null,"abstract":"<div><div>In this paper, the local discontinuous Galerkin (LDG) method is used to solve the fourth-order time-fractional sub-diffusion model with the Caputo–Fabrizio fractional derivative. Based on the generalized alternating numerical flux, we derive the fully discrete LDG scheme, the convergence order of our discrete scheme is <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>τ</mi></math></span>, <span><math><mi>h</mi></math></span> and <span><math><mi>k</mi></math></span> represent the time step size, space step size and polynomial degree, respectively. The stability and convergence of the proposed scheme are proved by mathematical induction. A numerical example is provided to verify the theoretical analysis and efficiency of the newly developed scheme.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109580"},"PeriodicalIF":2.9,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sign-changing solutions for a fractional Choquard system with strongly indefinite structure","authors":"Jianqing Chen, Qian Zhang","doi":"10.1016/j.aml.2025.109582","DOIUrl":"10.1016/j.aml.2025.109582","url":null,"abstract":"<div><div>In this paper, by using the generalized Nehari manifold and the principle of symmetric criticality, we prove the existence of sign-changing solutions to a class of fractional Choquard system with strongly indefinite structure.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109582"},"PeriodicalIF":2.9,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143877289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Persistence and extinction of a stochastic SVI epidemic model with standard incidence and reaction–diffusion","authors":"Tan Su, Yonggui Kao, Daqing Jiang","doi":"10.1016/j.aml.2025.109579","DOIUrl":"10.1016/j.aml.2025.109579","url":null,"abstract":"<div><div>Considering the important effects of population diffusion and vaccine ineffectiveness on disease transmission, a stochastic SVI (Susceptible–Vaccinated–Infected) epidemic model with reaction–diffusion is mainly investigated in this paper. We prove the existence of the unique global positive strong solution by an innovative variable transformation. The sufficient conditions for disease persistence and exponential extinction are also established by suitable Lyapunov functions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109579"},"PeriodicalIF":2.9,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Representation of solutions to a linear matrix discrete equation with single delay","authors":"Josef Diblík","doi":"10.1016/j.aml.2025.109577","DOIUrl":"10.1016/j.aml.2025.109577","url":null,"abstract":"<div><div>A linear matrix delayed discrete equation <span><span><span><math><mrow><mi>Δ</mi><mi>X</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mi>B</mi><mi>X</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mi>m</mi><mo>)</mo></mrow><mo>+</mo><mi>X</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mi>m</mi><mo>)</mo></mrow><mi>C</mi><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>is considered, where <span><math><mi>m</mi></math></span> is a fixed positive integer, <span><math><mrow><mi>k</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mspace></mspace></mrow></math></span> is a discrete independent variable, <span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> is an <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> unknown variable matrix, <span><math><mi>Δ</mi></math></span> is the first order forward difference, <span><math><mi>B</mi></math></span>, <span><math><mi>C</mi></math></span> are given <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> constant matrices, and <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> is a given <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> variable matrix. Using a special matrix function, under some commutativity conditions, formulas are derived, solving an initial problem <span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mi>Ψ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mi>m</mi><mo>,</mo><mo>−</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><mi>Ψ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> is an <span><math><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></math></span> variable matrix. Some connections with previously known results are discussed with open problems suggested for further investigations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109577"},"PeriodicalIF":2.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A time-delayed and drug-controlled within-host model","authors":"Yue Hou , Zhimin Li , Tailei Zhang","doi":"10.1016/j.aml.2025.109558","DOIUrl":"10.1016/j.aml.2025.109558","url":null,"abstract":"<div><div>In this paper, we present a within-host model incorporating time delays and drug control mechanisms to study the dynamics of infectious diseases. We begin by defining the basic reproduction number, <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, and subsequently prove that when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo><</mo><mn>1</mn></mrow></math></span>, the disease-free equilibrium is globally attractive; while for <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></mrow></math></span>, the disease persists uniformly. Numerical simulations are employed to validate our analytical findings.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109558"},"PeriodicalIF":2.9,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Large global solutions to the compressible flow of liquid crystals","authors":"Hui Ou, Hongyun Peng","doi":"10.1016/j.aml.2025.109578","DOIUrl":"10.1016/j.aml.2025.109578","url":null,"abstract":"<div><div>We construct the global large solutions for the compressible flow of liquid crystals in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. This class of data relax the smallness restriction imposed on the the initial incompressible velocity. Particularly, our work improves upon previous studies by Hu and Wu (2013) and Zhai (2025).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109578"},"PeriodicalIF":2.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fourier beyond dispersion: Wavenumber explicit and precise accuracy of FDMs for the Helmholtz equation","authors":"Hui Zhang","doi":"10.1016/j.aml.2025.109576","DOIUrl":"10.1016/j.aml.2025.109576","url":null,"abstract":"<div><div>We propose a practical tool for evaluating and comparing the accuracy of FDMs for the Helmholtz equation. The tool based on Fourier analysis makes it easy to find wavenumber explicit order of convergence, and can be used for rigorous proof. It fills in the gap between the dispersion analysis and the actual error with source term. We illustrate it for classical and some dispersion free schemes in 1D, with conclusions verified by numerical experiments.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109576"},"PeriodicalIF":2.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Feynman–Kac formula for regime-switching general diffusions","authors":"Zhiqiang Wei , Yejuan Wang , Erkan Nane","doi":"10.1016/j.aml.2025.109573","DOIUrl":"10.1016/j.aml.2025.109573","url":null,"abstract":"<div><div>The aim of this paper is to establish a version of the Feynman–Kac formula for a class of regime-switching general diffusion processes, in which the general diffusion part is a time-homogeneous Markov process (whose infinitesimal generator is the general diffusion including both Laplacian and Lévy operators). The classical method based on the Itô formula can no longer be used here due to the presence of the general diffusion process. Notably, an innovative method is introduced to deduce the infinitesimal generator of the regime-switching general diffusion process, which greatly contributes to the analyses on the global existence of solutions for the corresponding partial differential equation with external potential and forcing.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109573"},"PeriodicalIF":2.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143847741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integrable matrix nonlinear Schrödinger equations with reduced Lax pairs of AKNS type","authors":"Wen-Xiu Ma","doi":"10.1016/j.aml.2025.109574","DOIUrl":"10.1016/j.aml.2025.109574","url":null,"abstract":"<div><div>A specific class of Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problems is reduced using pairs of similarity transformations. The corresponding integrable hierarchies are derived from the reduced Lax pairs, extending the standard matrix AKNS integrable hierarchies. A few illustrative examples are provided to showcase the diversity of matrix integrable nonlinear Schrödinger equations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109574"},"PeriodicalIF":2.9,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stationary distribution and extinction of a stochastic HIV/AIDS model with screened disease carriers, standard incidence rate and Ornstein–Uhlenbeck process","authors":"Wenjie Zuo, Shengnan Jiang","doi":"10.1016/j.aml.2025.109575","DOIUrl":"10.1016/j.aml.2025.109575","url":null,"abstract":"<div><div>This paper proposes a stochastic HIV/AIDS model that includes screening for virus carriers and infected individuals actively seeking treatment, with the average number of sexual partners <span><math><mover><mrow><mi>k</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> controlled by a log-normal Ornstein–Uhlenbeck process. By constructing appropriate Lyapunov functions, the existence of a stationary distribution is obtained. Additionally, we establish sufficient condition for the extinction of the diseases, thereby offering valuable insights into AIDS control and policy decisions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"168 ","pages":"Article 109575"},"PeriodicalIF":2.9,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143835144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}