Fractional Calculus and Applied Analysis最新文献

Infinitely many solutions for impulsive fractional Schrödinger-Kirchhoff-type equations involving p-Laplacian via variational method

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

引用次数: 0

Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems

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

引用次数: 0

Topological properties of the solution set for Caputo fractional evolution inclusions involving delay

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

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

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

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

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

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

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

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