Fractional Calculus and Applied Analysis最新文献_第9页

Searching for Sonin kernels 搜索索宁核仁

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-08-07 DOI: 10.1007/s13540-024-00321-0

Manuel D. Ortigueira

引用次数: 0

Attractors of Caputo semi-dynamical systems 卡普托半动力系统的吸引子

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-08-07 DOI: 10.1007/s13540-024-00324-x

T. S. Doan, P. E. Kloeden

引用次数: 0

Optimization of the shape for a non-local control problem 优化非局部控制问题的形状

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-08-07 DOI: 10.1007/s13540-024-00318-9

Zhiwei Cheng, Hayk Mikayelyan

引用次数: 0

Regularization of an inverse source problem for fractional diffusion-wave equations under a general noise assumption 一般噪声假设下分数扩散波方程反源问题的正规化

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-08-06 DOI: 10.1007/s13540-024-00315-y

Dinh Nguyen Duy Hai, Le Van Chanh

{"title":"Regularization of an inverse source problem for fractional diffusion-wave equations under a general noise assumption","authors":"Dinh Nguyen Duy Hai, Le Van Chanh","doi":"10.1007/s13540-024-00315-y","DOIUrl":"https://doi.org/10.1007/s13540-024-00315-y","url":null,"abstract":"We consider the ill-posed inverse problem of determining an unknown source term appearing in abstract fractional diffusion-wave equations from a general noise assumption. Based on a Hölder-type source condition, we give the theoretical order optimality as well as the conditional stability result. To solve the problem, we propose fractional filter regularization methods, which can be regarded as an extension of the classical Tikhonov and Landweber methods. The idea is first to transform the problem into an ill-posed operator equation, then construct the regularization methods for the operator equation by introducing a suitable fractional filter function. As a natural further step, we study the convergence of the regularization methods, for which we derive order optimal rates of convergence under both a priori and a posteriori parameter choice rules. Applications of our fractional filter functions to both the fractional Tikhonov and the fractional Landweber filters are also investigated. Finally, three numerical examples in one-dimensional and two-dimensional cases are tested to validate our theoretical results.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"72 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141899470","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

Multiplicity of solutions for fractional Hamiltonian systems with combined nonlinearities and without coercive conditions 具有组合非线性且无强制条件的分数哈密顿系统解的多重性

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-08-05 DOI: 10.1007/s13540-024-00320-1

Mohsen Timoumi

引用次数: 0

Least fractional order memristor nonlinearity to exhibits chaos in a hidden hyperchaotic system 最小分数阶记忆晶闸管非线性在隐藏超混沌系统中显示混沌

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-08-05 DOI: 10.1007/s13540-024-00319-8

S. Sabarathinam, D. Aravinthan, Viktor Papov, R. Vadivel, N. Gunasekaran

引用次数: 0

Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals 通过全等立方的局部特殊约翰-尼伦伯格-坎帕纳托空间及其在局部卡尔德龙-齐格蒙德奇异积分和分数积分的有界性中的应用

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-07-15 DOI: 10.1007/s13540-024-00307-y

Junan Shi, Hongchao Jia, Dachun Yang

{"title":"Localized special John–Nirenberg–Campanato spaces via congruent cubes with applications to boundedness of local Calderón–Zygmund singular integrals and fractional integrals","authors":"Junan Shi, Hongchao Jia, Dachun Yang","doi":"10.1007/s13540-024-00307-y","DOIUrl":"https://doi.org/10.1007/s13540-024-00307-y","url":null,"abstract":"Let (p,qin [1,infty )), s be a nonnegative integer, (alpha in mathbb {R}), and (mathcal {X}) be (mathbb {R}^n) or a cube (Q_0subsetneqq mathbb {R}^n). In this article, the authors introduce the localized special John–Nirenberg–Campanato spaces via congruent cubes, (jn_{(p,q,s)_{alpha }}^{textrm{con}}(mathcal {X})), and show that, when (pin (1,infty )), the predual of (jn_{(p,q,s)_{alpha }}^{textrm{con}}(mathcal {X})) is a Hardy-kind space (hk_{(p',q',s)_{alpha }}^{textrm{con}}(mathcal {X})), where (frac{1}{p}+frac{1}{p'}=1=frac{1}{q}+frac{1}{q'}). As applications, in the case (mathcal {X}=mathbb {R}^n), the authors obtain the boundedness of local Calderón–Zygmund singular integrals and local fractional integrals on both (jn_{(p,q,s)_{alpha }}^{textrm{con}}(mathbb {R}^n)) and (hk_{(p,q,s)_{alpha }}^{textrm{con}}(mathbb {R}^n)). One novelty of this article is to find the appropriate expression of local Calderón–Zygmund singular integrals on (jn_{(p,q,s)_{alpha }}^{textrm{con}}(mathbb {R}^n)) and the other novelty is that, for the boundedness on (hk_{(p,q,s)_{alpha }}^{textrm{con}}(mathbb {R}^n)), the authors use the duality theorem to overcome the essential difficulties caused by the deficiency of both the molecular and the maximal function characterizations of (hk_{(p,q,s)_{alpha }}^{textrm{con}}(mathbb {R}^n)).","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"66 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141625072","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 Taylor’s formulas in fractional calculus: overview and characterization for the Caputo derivative 关于分数微积分中的泰勒公式：概述和卡普托导数的特征描述

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-07-08 DOI: 10.1007/s13540-024-00311-2

Roberto Nuca, Matteo Parsani

引用次数: 0

A necessary and sufficient conditions for the global existence of solutions to fractional reaction-diffusion equations on $$mathbb {R}^{N}$$ 分式反应扩散方程在 $$mathbb {R}^{N}$$ 上全局存在解的必要条件和充分条件

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-07-01 DOI: 10.1007/s13540-024-00310-3

Soon-Yeong Chung, Jaeho Hwang

{"title":"A necessary and sufficient conditions for the global existence of solutions to fractional reaction-diffusion equations on $$mathbb {R}^{N}$$","authors":"Soon-Yeong Chung, Jaeho Hwang","doi":"10.1007/s13540-024-00310-3","DOIUrl":"https://doi.org/10.1007/s13540-024-00310-3","url":null,"abstract":"A necessary and sufficient condition for the existence or nonexistence of global solutions to the following fractional reaction-diffusion equations $$begin{aligned} {left{ begin{array}{ll} u_{t}=Delta _{alpha } u + psi (t)f(u),,,&{} text{ in } mathbb {R}^{N}times (0,infty ), u(cdot ,0)=u_{0}ge 0,,,&{} text{ in } mathbb {R}^{N}, end{array}right. } end{aligned}$$has not been known and remained as an open problem for a few decades, where (Nge 2), (Delta _{alpha }=-left( -Delta right) ^{alpha /2}) denotes the fractional Laplace operator with (0<alpha le 2), (psi ) is a nonnegative and continuous function, and f is a convex function. The purpose of this paper is to resolve this problem completely as follows: $$begin{aligned} begin{aligned}&text{ There } text{ is } text{ a } text{ global } text{ solution } text{ to } text{ the } text{ equation } text{ if } text{ and } text{ only } text{ if }&hspace{20mm}int _{1}^{infty }psi (t)t^{frac{N}{alpha }}fleft( epsilon , t^{-frac{N}{alpha }}right) dt<infty ,&text{ for } text{ some } epsilon >0. end{aligned} end{aligned}$$","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"76 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489643","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

Fractional Fokker-Planck-Kolmogorov equations with Hölder continuous drift 霍尔德连续漂移的分数福克-普朗克-科尔莫戈罗夫方程

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-07-01 DOI: 10.1007/s13540-024-00309-w

Rongrong Tian, Jinlong Wei

引用次数: 0