Fractional Calculus and Applied Analysis最新文献_第5页

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

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":"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).This work is an extended and supplemented version of the paper presented at ICFDA 2024 at Bordeaux University, July 2024 (see [27]).","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":"We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity $$begin{aligned} mathfrak {M}left( int _{Q}frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdyright) (-Delta )_{p}^{s} u&=frac{lambda }{u^{gamma }}+u^{p_s^*-1}~text {in}~Omega , u&>0~text {in}~Omega , u&=0~text {in}~mathbb {R}^Nsetminus Omega , end{aligned}$$where (mathfrak {M}) is the Kirchhoff function, (Q=mathbb {R}^{2N}setminus ((mathbb {R}^Nsetminus Omega )times (mathbb {R}^Nsetminus Omega ))), (Omega subset mathbb {R}^N), is a bounded domain with Lipschitz boundary, (lambda >0), (N>ps), (0<s,gamma <1), ((-Delta )_{p}^{s}) is the fractional p-Laplacian for (1<p<infty ) and (p_s^*=frac{Np}{N-ps}) is the critical Sobolev exponent. We employ a cut-off argument to obtain the existence of k (being arbitrarily large integer) solutions. Furthermore, by using the Moser iteration technique, we prove an uniform (L^{infty }({Omega })) 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","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

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

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

引用次数: 0

On fractional differential inclusion with damping driven by variational-hemivariational inequality 由变分-半变分不等式驱动的带阻尼的分数阶微分包含

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-01-29 DOI: 10.1007/s13540-025-00375-8

Yunshui Liang, Lu-Chuan Ceng, Shengda Zeng

引用次数: 0

On a uniqueness criterion for nonlinear fractional differential equations 非线性分数阶微分方程的唯一性准则

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-01-24 DOI: 10.1007/s13540-025-00374-9

Nguyen Minh Dien

引用次数: 0

Cauchy problem for time-space fractional incompressible Navier-Stokes equations in $$mathbb {R}^n$$ 时空分式不可压缩Navier-Stokes方程的Cauchy问题 $$mathbb {R}^n$$

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-01-21 DOI: 10.1007/s13540-025-00373-w

Miao Yang, Li-Zhen Wang, Lu-Sheng Wang

引用次数: 0

Existence and approximate controllability of Hilfer fractional impulsive evolution equations Hilfer分数阶脉冲演化方程的存在性及近似可控性

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-01-17 DOI: 10.1007/s13540-025-00372-x

Kee Qiu, Michal Fečkan, JinRong Wang

引用次数: 0