Fractional Calculus and Applied Analysis最新文献

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Investigation of controllability criteria for Caputo fractional dynamical systems with delays in both state and control 状态和控制均有时滞的Caputo分数阶动力系统的可控性准则研究
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-03-14 DOI: 10.1007/s13540-025-00387-4
Anjapuli Panneer Selvam, Venkatesan Govindaraj
{"title":"Investigation of controllability criteria for Caputo fractional dynamical systems with delays in both state and control","authors":"Anjapuli Panneer Selvam, Venkatesan Govindaraj","doi":"10.1007/s13540-025-00387-4","DOIUrl":"https://doi.org/10.1007/s13540-025-00387-4","url":null,"abstract":"<p>This study examines the controllability criteria for linear and semilinear fractional dynamical systems with delays in both state and control variables in the framework of the Caputo fractional derivative. To establish the controllability criteria for linear fractional dynamical systems, the study derives necessary and sufficient conditions by employing the positive definiteness of the Grammian matrix. Extending this analysis to semilinear fractional dynamical systems, Krasnoselskii’s fixed point theorem is employed to derive sufficient conditions for the existence of a solution. Furthermore, in addressing semilinear fractional dynamical systems with delays in both state and control, Banach’s fixed point theorem is employed to derive sufficient conditions for the existence of a solution. In order to enhance the comprehension of the theoretical results, the study presents three specific examples along with appropriate graphical representations.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"9 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143627619","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}
引用次数: 0
On fractional derivatives of Djrbashian–Nersessian type with the nth-level Sonin kernels and their basic properties 具有n级Sonin核的djbashian - nersessian型的分数阶导数及其基本性质
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-03-14 DOI: 10.1007/s13540-025-00385-6
Mohammed Al-Refai, Yuri Luchko
{"title":"On fractional derivatives of Djrbashian–Nersessian type with the nth-level Sonin kernels and their basic properties","authors":"Mohammed Al-Refai, Yuri Luchko","doi":"10.1007/s13540-025-00385-6","DOIUrl":"https://doi.org/10.1007/s13540-025-00385-6","url":null,"abstract":"<p>In this paper, we introduce a concept of the <i>n</i>th-level general fractional derivatives that combine the Djrbashian–Nersessian fractional derivatives and the general fractional derivatives with the Sonin kernels in one definition. Then some basic properties of these fractional derivatives including the fundamental theorems of fractional calculus and a formula for their Laplace transform are presented. As an example, all results derived for the <i>n</i>th-level general fractional derivatives are demonstrated on the important particular case of the Djrbashian–Nersessian fractional derivative.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"22 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143627618","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}
引用次数: 0
Infinitely many solutions for impulsive fractional Schrödinger-Kirchhoff-type equations involving p-Laplacian via variational method 用变分方法求解脉冲分数阶Schrödinger-Kirchhoff-type方程的无穷多解
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-03-05 DOI: 10.1007/s13540-025-00380-x
Yi Wang, Lixin Tian
{"title":"Infinitely many solutions for impulsive fractional Schrödinger-Kirchhoff-type equations involving p-Laplacian via variational method","authors":"Yi Wang, Lixin Tian","doi":"10.1007/s13540-025-00380-x","DOIUrl":"https://doi.org/10.1007/s13540-025-00380-x","url":null,"abstract":"<p>In this paper, we provide new multiplicity results for a class of impulsive fractional Schrödinger-Kirchhoff-type equations involving <i>p</i>-Laplacian and Riemann-Liouville derivatives. By using the variational method and critical point theory, we obtain that the impulsive fractional problem has infinitely many solutions under appropriate hypotheses when the parameter <span>(lambda )</span> lies in different intervals.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"16 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546505","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}
引用次数: 0
Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems 二维非自治Reissner-Mindlin-Timoshenko板系的回拉动力学
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-03-04 DOI: 10.1007/s13540-025-00383-8
Baowei Feng, Mirelson M. Freitas, Anderson J. A. Ramos, Manoel J. Dos Santos
{"title":"Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems","authors":"Baowei Feng, Mirelson M. Freitas, Anderson J. A. Ramos, Manoel J. Dos Santos","doi":"10.1007/s13540-025-00383-8","DOIUrl":"https://doi.org/10.1007/s13540-025-00383-8","url":null,"abstract":"<p>In this paper, we are concerned with 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems with Laplacian damping terms and nonlinear sources terms. The global well-posedness is proved by using the theory of maximal monotone operators. And then we get the Lipschtiz stability of the solution. By establishing the existence of pullback absorbing sets and pullback asymptotic compactness of the process generated by the system, we obtain the existence of pullback attractors. The upper-semicontinuity of pullback attractors regarding the fractional exponent is also proved. It is the first time when the non-autonomous Reissner-Mindlin-Timoshenko plate systems are studied.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"22 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546175","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}
引用次数: 0
Topological properties of the solution set for Caputo fractional evolution inclusions involving delay 涉及延迟的Caputo分数演化内含物解集的拓扑性质
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-03-04 DOI: 10.1007/s13540-024-00362-5
Huihui Yang, He Yang
{"title":"Topological properties of the solution set for Caputo fractional evolution inclusions involving delay","authors":"Huihui Yang, He Yang","doi":"10.1007/s13540-024-00362-5","DOIUrl":"https://doi.org/10.1007/s13540-024-00362-5","url":null,"abstract":"<p>This article studies topological properties of the solution set for a class of Caputo fractional delayed evolution inclusions. Firstly, in the scenario when the cosine family is noncompact, the compactness and <span>(R_{delta })</span>-property are obtained for the mild solution set. Then, as an application of the above obtained results, the approximative controllability is demonstrated. Finally, an example is given as an illustration.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"13 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143546176","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}
引用次数: 0
Revisiting distributed order PID controller 重访分布式顺序PID控制器
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-02-26 DOI: 10.1007/s13540-025-00381-w
Milan R. Rapaić, Zoran D. Jeličić, Tomislav B. Šekara, Rachid Malti, Vukan Turkulov, Mirna N. Radović
{"title":"Revisiting distributed order PID controller","authors":"Milan R. Rapaić, Zoran D. Jeličić, Tomislav B. Šekara, Rachid Malti, Vukan Turkulov, Mirna N. Radović","doi":"10.1007/s13540-025-00381-w","DOIUrl":"https://doi.org/10.1007/s13540-025-00381-w","url":null,"abstract":"<p>The paper addresses structural properties of distributed order controllers. A Distributed Order PID (DOPID) controller is a control structure in which a continuum of “differintegral” actions of orders between -1 and 1 are integrated together, and where relative contributions of different orders is determined by a weighting function. This stands in sharp contrast to conventional proportional-integral-derivative controllers, or even fractional order PID (FPID) controller and multi-term FPID, in which discrete actions appear only and a finite set of real parameters, controller gains, are sufficient to specify contributions of each action. The paper presents an in-depth analysis of the DOPID controller, emphasizing its theoretical properties and distinctions with integer and fractional order PID. It is shown that DOPID can be considered a generalization of these controllers only if the weighting function is a sequence of Dirac pulses. Some structural deficiencies of DOPID in case of a wide class of weighting functions have been emphasized. A modified DOPID structure — which we refer to as the DOPID of the Second Kind — is proposed and analyzed as well. Among other things, it has been shown that such modified DOPID controller provides better generalization to discrete order controllers (PID and FPID).</p><p>This work is an extended and supplemented version of the paper presented at ICFDA 2024 at Bordeaux University, July 2024 (see [27]).</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"28 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143506851","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}
引用次数: 0
Existence of at least k solutions to a fractional p-Kirchhoff problem involving singularity and critical exponent 涉及奇点和临界指数的分数阶p-Kirchhoff问题至少k个解的存在性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-02-26 DOI: 10.1007/s13540-025-00382-9
Sekhar Ghosh, Debajyoti Choudhuri, Alessio Fiscella
{"title":"Existence of at least k solutions to a fractional p-Kirchhoff problem involving singularity and critical exponent","authors":"Sekhar Ghosh, Debajyoti Choudhuri, Alessio Fiscella","doi":"10.1007/s13540-025-00382-9","DOIUrl":"https://doi.org/10.1007/s13540-025-00382-9","url":null,"abstract":"<p>We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity </p><span>$$begin{aligned} mathfrak {M}left( int _{Q}frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdyright) (-Delta )_{p}^{s} u&amp;=frac{lambda }{u^{gamma }}+u^{p_s^*-1}~text {in}~Omega , u&amp;&gt;0~text {in}~Omega , u&amp;=0~text {in}~mathbb {R}^Nsetminus Omega , end{aligned}$$</span><p>where <span>(mathfrak {M})</span> is the Kirchhoff function, <span>(Q=mathbb {R}^{2N}setminus ((mathbb {R}^Nsetminus Omega )times (mathbb {R}^Nsetminus Omega )))</span>, <span>(Omega subset mathbb {R}^N)</span>, is a bounded domain with Lipschitz boundary, <span>(lambda &gt;0)</span>, <span>(N&gt;ps)</span>, <span>(0&lt;s,gamma &lt;1)</span>, <span>((-Delta )_{p}^{s})</span> is the fractional <i>p</i>-Laplacian for <span>(1&lt;p&lt;infty )</span> and <span>(p_s^*=frac{Np}{N-ps})</span> is the critical Sobolev exponent. We employ a <i>cut-off</i> argument to obtain the existence of <i>k</i> (being arbitrarily large integer) solutions. Furthermore, by using the Moser iteration technique, we prove an uniform <span>(L^{infty }({Omega }))</span> bound for the solutions. The novelty of this work lies in proving the existence of small energy solutions by using symmetric mountain pass theorem in spite of the presence of a critical nonlinear term which, of course, is super-linear.\u0000</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"102 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143506850","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}
引用次数: 0
On positive solutions of fractional elliptic equations with oscillating nonlinearity 具有非线性振荡的分数阶椭圆方程的正解
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-02-21 DOI: 10.1007/s13540-025-00379-4
Francisco J. S. A. Corrêa, César E. T. Ledesma, Alânnio B. Nóbrega
{"title":"On positive solutions of fractional elliptic equations with oscillating nonlinearity","authors":"Francisco J. S. A. Corrêa, César E. T. Ledesma, Alânnio B. Nóbrega","doi":"10.1007/s13540-025-00379-4","DOIUrl":"https://doi.org/10.1007/s13540-025-00379-4","url":null,"abstract":"<p>This paper investigates the existence and multiplicity of positive solutions to the following semilinear problem: </p><p> where <span>(fin C([0,infty ),{mathbb {R}}))</span> represents an oscillating nonlinearity that satisfies a type of area condition. Our main analytical tools include variational methods and the sub-supersolution method.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"13 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143470738","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}
引用次数: 0
$$psi $$ -Hilfer type linear fractional differential equations with variable coefficients $$psi $$ 变系数的hilfer型线性分数阶微分方程
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-02-18 DOI: 10.1007/s13540-025-00378-5
Fang Li, Huiwen Wang
{"title":"$$psi $$ -Hilfer type linear fractional differential equations with variable coefficients","authors":"Fang Li, Huiwen Wang","doi":"10.1007/s13540-025-00378-5","DOIUrl":"https://doi.org/10.1007/s13540-025-00378-5","url":null,"abstract":"<p>In this study, we establish an explicit representation of solutions to <span>(psi )</span>-Hilfer type linear fractional differential equations with variable coefficients in weighted spaces. Furthermore, we prove the existence and uniqueness of solutions for these equations. As a special case, we derive corresponding results for <span>(psi )</span>-fractional differential equations with variable coefficients. To demonstrate the practical applications of our theoretical results, we derive explicit solutions for several representative cases, including the voltmeter equation in electrochemistry, the equation around an <span>(alpha )</span>-ordinary point, and the fractional Ayre equation. Furthermore, we provide numerical simulations.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"4 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444018","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}
引用次数: 0
Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization 具有Sturm-Liouville型空间分数阶导数的度量星图上的时空分数抛物方程:分析与离散化
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-31 DOI: 10.1007/s13540-025-00376-7
Vaibhav Mehandiratta, Mani Mehra
{"title":"Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization","authors":"Vaibhav Mehandiratta, Mani Mehra","doi":"10.1007/s13540-025-00376-7","DOIUrl":"https://doi.org/10.1007/s13540-025-00376-7","url":null,"abstract":"<p>In this paper, we study the well-posedness and discretization of the space-time fractional parabolic equations (STFPEs) of the Sturm-Liouville type on a metric star graph. The considered problem involves the fractional time derivative in the Caputo sense, and the spatial fractional derivative is of the Sturm-Liouville type consisting of the composition of the right-sided Caputo derivative and left-sided Riemann-Liouville fractional derivative. By introducing the appropriate function spaces for the involved fractional operators in both the time and spatial variable, we prove the well-posedness of the weak solution of the considered STFPEs by using the Galerkin approximation method. Moreover, we propose a difference scheme to find the numerical solution of the STFPEs on a metric star graph by approximating the Caputo time derivative using the L1 method and spatial fractional derivative with the Grünwald-Letnikov formula. Finally, we illustrate the performance and the accuracy of the proposed difference scheme via examples.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"60 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071529","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}
引用次数: 0
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