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Mathematical Methods in the Applied Sciences最新文献

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Hopf bifurcation analysis of a two‐delayed diffusive predator–prey model with spatial memory of prey 具有猎物空间记忆的双延迟扩散捕食者-猎物模型的霍普夫分岔分析
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-27 DOI: 10.1002/mma.10416
Hongyan Wang, Yunxian Dai, Shumin Zhou
{"title":"Hopf bifurcation analysis of a two‐delayed diffusive predator–prey model with spatial memory of prey","authors":"Hongyan Wang, Yunxian Dai, Shumin Zhou","doi":"10.1002/mma.10416","DOIUrl":"https://doi.org/10.1002/mma.10416","url":null,"abstract":"In this paper, we consider a diffusive predator–prey model with <jats:styled-content>spatial</jats:styled-content> memory of prey and gestation delay of predator. For the system without delays, we study the stability of the positive equilibrium in the case of diffusion and no diffusion, respectively. For the delayed model without diffusions, the existence of Hopf bifurcation is discussed. Further, we investigate the stability switches of the model with delays and diffusions when two delays change simultaneously by calculating the stability switching curves and obtain the existence of Hopf bifurcation. We also calculate the normal form of Hopf bifurcation to determine the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, numerical simulations verify the theoretical results.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220097","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}
引用次数: 0
Editorial for special issue “Current trends in Applied Mathematics” 应用数学的当前趋势 "特刊编辑
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-26 DOI: 10.1002/mma.10360
Gerassimos Barbatis, Athanasios Yannacopoulos
{"title":"Editorial for special issue “Current trends in Applied Mathematics”","authors":"Gerassimos Barbatis,&nbsp;Athanasios Yannacopoulos","doi":"10.1002/mma.10360","DOIUrl":"10.1002/mma.10360","url":null,"abstract":"","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220091","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}
引用次数: 0
Retrieval of the optical soliton solutions of the perturbed Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity having the spatio‐temporal dispersion 具有广义反立方律非线性时空色散的扰动薛定谔-希罗塔方程的光孤子解的检索
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-24 DOI: 10.1002/mma.10429
Ismail Onder, Aydin Secer, Muslum Ozisik, Mustafa Bayram
{"title":"Retrieval of the optical soliton solutions of the perturbed Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity having the spatio‐temporal dispersion","authors":"Ismail Onder, Aydin Secer, Muslum Ozisik, Mustafa Bayram","doi":"10.1002/mma.10429","DOIUrl":"https://doi.org/10.1002/mma.10429","url":null,"abstract":"In this study, we obtained optical soliton solutions of the perturbed nonlinear Schrödinger–Hirota equation with generalized anti‐cubic law nonlinearity in the presence of spatio‐temporal dispersion. This equation models the propagation of optical pulses in fiber optic cables. Due to the anti‐cubic nonlinearity, perturbation, and spatio‐temporal dispersion present in the model, it provides more accurate results for high‐speed and long‐distance transmissions. Given the significant developments in the field of optics, studies on complex equations such as this model are of great importance. With the increase in real‐life applications, obtaining solutions to optical equations has become crucial. In this study, we used the improved F‐expansion method to derive the optical soliton solutions for the relevant model. This technique allows for obtaining various solutions through the Jacobi elliptic auxiliary functions it employs. The obtained solutions consist of trigonometric and hyperbolic functions. As a result of the application, 10 solutions were obtained, and 2D and 3D graphics of these solutions are included. These graphs illustrate the motion directions of optical solitons and the effect of the nonlinearity parameter and spatio‐temporal dispersion parameter on soliton behavior. No restrictions were encountered during the study. Finally, the originality of the study lies in the first application of this technique to the relevant model and in examining the effect of the parameters and on this model.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220096","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}
引用次数: 0
Critical exponent for global solutions in a fourth‐order hyperbolic equation of p‐Kirchhoff type p-Kirchhoff 型四阶双曲方程全局解的临界指数
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-23 DOI: 10.1002/mma.10438
Bingchen Liu, Jiaxin Dou
{"title":"Critical exponent for global solutions in a fourth‐order hyperbolic equation of p‐Kirchhoff type","authors":"Bingchen Liu, Jiaxin Dou","doi":"10.1002/mma.10438","DOIUrl":"https://doi.org/10.1002/mma.10438","url":null,"abstract":"We study a fourth‐order hyperbolic equation involving Kirchhoff type ‐Laplacian and superlinear source, subject to zero Navier boundary condition, <jats:disp-formula> </jats:disp-formula>where is an open bounded domain in with ; denotes the maximal existence time; and and are constants. For , using auxiliary function method and Sobolev inequality, we prove that there are only global solutions. For , we obtain the optimal classification of initial energy and Nehari energy, which guarantees the existence of blow‐up solutions and global solutions. In the critical case , we find out that the coefficients of the Kirchhoff term and the superlinear source play important role in separating out the property of weak solutions.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220099","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}
引用次数: 0
Existence results for the generalized Riemann–Liouville type fractional Fisher‐like equation on the half‐line 半线上广义黎曼-刘维尔型分数费雪方程的存在性结果
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-10 DOI: 10.1002/mma.10398
N. Nyamoradi, Bashir Ahmad
{"title":"Existence results for the generalized Riemann–Liouville type fractional Fisher‐like equation on the half‐line","authors":"N. Nyamoradi, Bashir Ahmad","doi":"10.1002/mma.10398","DOIUrl":"https://doi.org/10.1002/mma.10398","url":null,"abstract":"In this paper, we discuss the existence of multiplicity of positive solutions to a new generalized Riemann–Liouville type fractional Fisher‐like equation on a semi‐infinite interval equipped with nonlocal multipoint boundary conditions involving Riemann–Liouville fractional derivative and integral operators. The existence of at least two positive solutions for the given problem is established by using the concept of complete continuity and iterative positive solutions. We show the existence of at least three positive solutions to the problem at hand by applying the generalized Leggett–Williams fixed‐point theorem due to Bai and Ge [Z. Bai, B. Ge, Existence of three positive solutions for some second‐order boundary value problems, Comput. Math. Appl. 48 (2014) 699‐70]. Illustrative examples are constructed to demonstrate the effectiveness of the main results. It has also been indicated in Section 5 that some new results appear as special cases by choosing the parameters involved in the given problem appropriately.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141921135","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}
引用次数: 0
Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions 由布朗运动和分数布朗运动驱动的随机半线性微分方程在有限维分布中的贝西科维奇近似自形解
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-09 DOI: 10.1002/mma.10403
Yongkun Li, Zhicong Bai
{"title":"Besicovitch almost automorphic solutions in finite‐dimensional distributions to stochastic semilinear differential equations driven by both Brownian and fractional Brownian motions","authors":"Yongkun Li, Zhicong Bai","doi":"10.1002/mma.10403","DOIUrl":"https://doi.org/10.1002/mma.10403","url":null,"abstract":"In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite‐dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite‐dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141922964","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}
引用次数: 0
Determining the order of time and spatial fractional derivatives 确定时间和空间分数导数的阶次
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-09 DOI: 10.1002/mma.10393
Ravshan Ashurov, Ilyoskhuja Sulaymonov
{"title":"Determining the order of time and spatial fractional derivatives","authors":"Ravshan Ashurov, Ilyoskhuja Sulaymonov","doi":"10.1002/mma.10393","DOIUrl":"https://doi.org/10.1002/mma.10393","url":null,"abstract":"The paper considers the initial‐boundary value problem for equation , in an N‐dimensional domain with a homogeneous Dirichlet condition. The fractional derivative is taken in the sense of Caputo. The main goal of the work is to solve the inverse problem of simultaneously determining two parameters: the order of the fractional derivative and the degree of the Laplace operator . A new formulation and solution method for this inverse problem are proposed. It is proved that in the new formulation the solution to the inverse problem exists and is unique for an arbitrary initial function from the class . Note that in previously known works, only the uniqueness of the solution to the inverse problem was proved and the initial function was required to be sufficiently smooth and non‐negative.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934956","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}
引用次数: 0
Mittag‐Leffler type functions of three variables 三变量的 Mittag-Leffler 型函数
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-09 DOI: 10.1002/mma.10401
A. Hasanov, Hilola Yuldashova
{"title":"Mittag‐Leffler type functions of three variables","authors":"A. Hasanov, Hilola Yuldashova","doi":"10.1002/mma.10401","DOIUrl":"https://doi.org/10.1002/mma.10401","url":null,"abstract":"In this article, we generalized Mittag‐Leffler‐type functions \u0000, and \u0000, which correspond, respectively, to the familiar Lauricella hypergeometric functions \u0000, and \u0000 of three variables. Initially, from the Mittag‐Leffler type function in the simplest form to the functions we are studying, necessary information about the development history, study, and importance of this and hypergeometric type functions will be introduced. Among the various properties and characteristics of these three‐variable Mittag‐Leffler‐type function \u0000, which we investigate in the article, include their relationships with other extensions and generalizations of the classical Mittag‐Leffler functions, their three‐dimensional convergence regions, their Euler‐type integral representations, their Laplace transforms, and their connections with the Riemann‐Liouville operators of fractional calculus. The link of three‐variable Mittag‐Leffler function with fractional differential equation systems involving different fractional orders is necessary on certain applications in physics.Therefore, we provide the systems of partial differential equations which are associated with them.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141921941","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}
引用次数: 0
Dual Cartan numbers and pseudo‐null lines 双卡坦数和伪空行
IF 2.1 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-08 DOI: 10.1002/mma.10323
İskender Öztürk
{"title":"Dual Cartan numbers and pseudo‐null lines","authors":"İskender Öztürk","doi":"10.1002/mma.10323","DOIUrl":"https://doi.org/10.1002/mma.10323","url":null,"abstract":"The study aims to introduce some geometric properties of dual Cartan numbers. Since a unit timelike Cartan number with lightlike vector part corresponds to a parabolic rotation around a lightlike axis, it has been shown that the unit dual Cartan number with lightlike dual vector also corresponds to a parabolic rotation and a translation transformation in the Cartan frame. Also, the angle between the directed pseudo‐null lines that tangent the same parabola is defined. Thus, the rotation and translation relationship between two directed pseudo‐null lines is obtained. Also, the E. Study transformation is given for the directed pseudo‐null lines.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929598","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}
引用次数: 0
Stability and optimal decay estimates for the 3D anisotropic Boussinesq equations 三维各向异性布辛斯方程的稳定性和最优衰减估计
IF 2.9 3区 数学
Mathematical Methods in the Applied Sciences Pub Date : 2024-08-08 DOI: 10.1002/mma.10391
Wan‐Rong Yang, Meng‐Zhen Peng
{"title":"Stability and optimal decay estimates for the 3D anisotropic Boussinesq equations","authors":"Wan‐Rong Yang, Meng‐Zhen Peng","doi":"10.1002/mma.10391","DOIUrl":"https://doi.org/10.1002/mma.10391","url":null,"abstract":"This paper focuses on the three‐dimensional (3D) incompressible anisotropic Boussinesq system while the velocity of fluid only involves horizontal dissipation and the temperature has a damping term. By utilizing the structure of the system, the energy methods and the means of bootstrapping argument, we prove the global stability property in the Sobolev space of perturbations near the hydrostatic equilibrium. Moreover, we take an effective approach to obtain the optimal decay rates for the global solution itself as well as its derivatives. In this paper, we aim to reveal the mechanism of how the temperature helps stabilize the fluid. Additionally, exploring the stability of perturbations near hydrostatic equilibrium may provide valuable insights into specific severe weather phenomena.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968798","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}
引用次数: 0
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