Mathematical Methods in the Applied Sciences最新文献

{"title":"Global stability in the Ricker model with delay and stocking","authors":"Ziyad AlSharawi,&nbsp;Sadok Kallel","doi":"10.1002/mma.10440","DOIUrl":"10.1002/mma.10440","url":null,"abstract":"<p>We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global stability of the equilibrium solution in the case of constant stocking, as well as the global stability of the 2-periodic solution in the case of 2-periodic stocking. Our approach extensively relies on the utilization of the embedding technique. Whether constant stocking or periodic stocking, the model has the potential to undergo a Neimark–Sacker bifurcation in both cases. However, the Neimark–Sacker bifurcation in the 2-periodic case results in the emergence of two invariant curves that collectively function as a single attractor. Finally, we pose open questions in the form of conjectures about global stability for certain choices of the parameters.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2370-2387"},"PeriodicalIF":2.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220255","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":"Solving a non-standard Optimal Control royalty payment problem using a new modified shooting method","authors":"Suliadi Firdaus Sufahani,&nbsp;Wan Noor Afifah Wan Ahmad,&nbsp;Kavikumar Jacob,&nbsp;Sharidan Shafie,&nbsp;Ruzairi Abdul Rahim,&nbsp;Mahmod Abd Hakim Mohamad,&nbsp;Mohd Saifullah Rusiman,&nbsp;Rozaini Roslan,&nbsp;Mohd Zulariffin Md Maarof,&nbsp;Muhamad Ali Imran Kamarudin","doi":"10.1002/mma.10457","DOIUrl":"10.1002/mma.10457","url":null,"abstract":"<p>This paper considers a non-standard Optimal Control problem that has an application in economics. The primary focus of this research is to solve the royalty problem, which has been categorized as a non-standard Optimal Control problem, where the final state value and its functional performance index value are unknown. A new continuous necessary condition is investigated for the final state value so that it will convert the final costate value into a non-zero value. The research analyzes the seven-stage royalty piecewise function, which is then approximated to continuous form with the help of the hyperbolic tangent function and solves the problem by using a new modified shooting method. This modified shooting method applies Sufahani–Ahmad–Newton–Brent–Royalty Algorithm and Sufahani-Ahmad-Powell-Brent-Royalty Algorithm. For a validation process, the results are compared with the existing methods such as Euler, Runge–Kutta, Trapezoidal, and Hermite–Simpson approximations, and the results show that the proposed method yields an accurate terminal state value.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2665-2685"},"PeriodicalIF":2.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220250","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 nonlocal Kirchhoff diffusion problem with singular potential and logarithmic nonlinearity","authors":"Zhong Tan,&nbsp;Yi Yang","doi":"10.1002/mma.10451","DOIUrl":"10.1002/mma.10451","url":null,"abstract":"<p>In this paper, we investigate the following fractional Kirchhoff-type pseudo parabolic equation driven by a nonlocal integro-differential operator \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>ℒ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {mathcal{L}}_K $$</annotation>\u0000 </semantics></math>: \u0000\u0000 </p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2561-2583"},"PeriodicalIF":2.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220065","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":"Convex combinations of some convergent sequences","authors":"Stevo Stević","doi":"10.1002/mma.10463","DOIUrl":"https://doi.org/10.1002/mma.10463","url":null,"abstract":"We consider the convex combinations , of a pair of sequences of real numbers and such that , converging to , and study the location of the limit inside the intervals , for every or for sufficiently large . We also investigate the same problem for the case of two corresponding sequences converging to . Among other results, we prove some, a bit, unexpected ones. Namely, for each , we determine the exact index at which the sequence changes the monotonicity, and we also determine the type of the monotonicity. A number of interesting remarks are also presented.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"8 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220044","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":"Nonexistence of solutions to quasilinear Schrödinger equations with a parameter","authors":"Hongwang Yu,&nbsp;Yunfeng Wei,&nbsp;Caisheng Chen,&nbsp;Qiang Chen","doi":"10.1002/mma.10452","DOIUrl":"10.1002/mma.10452","url":null,"abstract":"<p>This paper is concerned with the class of quasilinear Schrödinger equations: \u0000\u0000 </p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2584-2599"},"PeriodicalIF":2.1,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220049","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":"Wave propagation for the isentropic compressible Navier–Stokes/Allen–Cahn system","authors":"Yazhou Chen, Houzhi Tang, Yue Zhang","doi":"10.1002/mma.10458","DOIUrl":"https://doi.org/10.1002/mma.10458","url":null,"abstract":"We study the Cauchy problem for the three‐dimensional isentropic compressible Navier–Stokes/Allen–Cahn system, which models the phase transitions in two‐component patterns interacting with a compressible fluid. Under the assumption that the initial perturbation is small and decays spatially, we establish the global existence and the pointwise behavior of strong solutions to this nonconserved system. To deal with the source terms involving the phase variable, we employ the Green's function and space‐time weighted estimates. The analysis shows that the phase variable mainly contains the diffusion wave with exponential decaying amplitude over time, and consequently the density and momentum of the compressible fluid adhere to a generalized Huygens principle.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"57 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220046","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 matrix versions of the k analog of ℑ-incomplete Gauss hypergeometric functions and associated fractional calculus","authors":"Muneera Abdullah Qadha,&nbsp;Sarah Abdullah Qadha,&nbsp;Ahmed Bakhet","doi":"10.1002/mma.10382","DOIUrl":"10.1002/mma.10382","url":null,"abstract":"<p>In this paper, our aim is to introduce a new definition of (\u0000<span></span><math>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>ℑ</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>-incomplete Wright hypergeometric matrix functions (\u0000<span></span><math>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>ℑ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow></math>-IWHMFs) using the \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>-incomplete Pochhammer matrix symbol. First, we define the \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>-incomplete gamma matrix function and introduce the \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>-incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these \u0000<span></span><math>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>ℑ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow></math>-IWHMFs. We have also obtained some results regarding the \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow></math>-fractional calculus operators of these \u0000<span></span><math>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>ℑ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow></math>-IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the \u0000<span></span><math>\u0000 <mrow>\u0000 <mfenced>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>ℑ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow></math>-IWHMFs.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 1","pages":"1237-1255"},"PeriodicalIF":2.1,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220043","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":"Spectral methods utilizing generalized Bernstein-like basis functions for time-fractional advection–diffusion equations","authors":"Shahad Adil Taher Algazaa,&nbsp;Jamshid Saeidian","doi":"10.1002/mma.10390","DOIUrl":"10.1002/mma.10390","url":null,"abstract":"<p>This paper presents two methods for solving two-dimensional linear and nonlinear time-fractional advection–diffusion equations with Caputo fractional derivatives. To effectively manage endpoint singularities, we propose an advanced space-time Galerkin technique and a collocation spectral method, both employing generalized Bernstein-like basis functions (GBFs). The properties and behaviors of these functions are examined, highlighting their practical applications. The space-time spectral methods incorporate GBFs in the temporal domain and classical Bernstein polynomials in the spatial domain. Fractional equations frequently produce irregular solutions despite smooth input data due to their singular kernel. To address this, GBFs are applied to the time derivative and classical Bernstein polynomials to the spatial derivative. A thorough error analysis confirms the technique's accuracy and convergence, offering a robust theoretical basis. Numerical experiments validate the method, demonstrating its effectiveness in solving both linear and nonlinear time-fractional advection–diffusion equations.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1411-1429"},"PeriodicalIF":2.1,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220045","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":"Study of Caputo fractional derivative and Riemann–Liouville integral with different orders and its application in multi-term differential equations","authors":"Ghaus Ur Rahman,&nbsp;Dildar Ahmad,&nbsp;José Francisco Gómez-Aguilar,&nbsp;Ravi P. Agarwal,&nbsp;Amjad Ali","doi":"10.1002/mma.10392","DOIUrl":"10.1002/mma.10392","url":null,"abstract":"<p>In this article, we initially provided the relationship between the RL fractional integral and the Caputo fractional derivative of different orders. Additionally, it is clear from the literature that studies into boundary value problems involving multi-term operators have been conducted recently, and the aforementioned idea is used in the formulation of several novel models. We offer a unique coupled system of fractional delay differential equations with proper respect for the role that multi-term operators play in the research of fractional differential equations, taking into account the newly established solution for fractional integral and derivative. We also made the assumptions that connected integral boundary conditions would be added on top of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$$ n $$</annotation>\u0000 </semantics></math>-fractional differential derivatives. The requirements for the existence and uniqueness of solutions are also developed using fixed-point theorems. While analyzing various sorts of Ulam's stability results, the qualitative elements of the underlying model will also be examined. In the paper's final section, an example is given for purposes of demonstration.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"1464-1502"},"PeriodicalIF":2.1,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220047","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 solution of spherically symmetric compressible Navier–Stokes equations with bounded density and density-dependent viscosity","authors":"Xueyao Zhang","doi":"10.1002/mma.10433","DOIUrl":"10.1002/mma.10433","url":null,"abstract":"<p>We consider the compressible Navier–Stokes equations with viscosities \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>μ</mi>\u0000 <mo>(</mo>\u0000 <mi>ρ</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>ρ</mi>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>λ</mi>\u0000 <mo>(</mo>\u0000 <mi>ρ</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$$ mu left(rho right)&amp;amp;#x00026;#x0003D;rho, lambda left(rho right)&amp;amp;#x00026;#x0003D;0 $$</annotation>\u0000 </semantics></math> in bounded domains when the initial data are spherically symmetric, which covers the Saint-Venant model for the motion of shallow water. First, based on the exploitation of the one-dimensional feature of symmetric solutions, we prove the global existence of weak solutions with initial vacuum, where the upper bound of the density is obtained. Then, with more conditions imposed on the nonvacuum initial data, we obtain the global weak solution which is a strong one away from the symmetry center. The analysis allows for the possibility that a vacuum state emerges at the symmetry center; in particular, we give the uniform bound of the radius of the vacuum domain.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 2","pages":"2235-2252"},"PeriodicalIF":2.1,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220054","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}