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

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":null,"pages":null},"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":null,"pages":null},"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

Qualitative properties of fractional convolution elliptic and parabolic operators in Besov spaces 贝索夫空间中分数卷积椭圆和抛物线算子的定性特性

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-06-21 DOI: 10.1007/s13540-024-00302-3

Veli Shakhmurov, Rishad Shahmurov

引用次数: 0

An approximation theoretic revamping of fractal interpolation surfaces on triangular domains 三角形域上分形插值面的近似理论翻新

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-06-18 DOI: 10.1007/s13540-024-00305-0

P. Viswanathan

{"title":"An approximation theoretic revamping of fractal interpolation surfaces on triangular domains","authors":"P. Viswanathan","doi":"10.1007/s13540-024-00305-0","DOIUrl":"https://doi.org/10.1007/s13540-024-00305-0","url":null,"abstract":"The theory of fractal surfaces, in its basic setting, asserts the existence of a bivariate continuous function defined on a triangular domain. The extant literature on the construction of fractal surfaces over triangular domains use certain assumptions for the construction and deal primarily with the interpolation aspects. Working in the framework of fractal surfaces over triangular domains, this note has a two-fold target. Firstly, to revamp the existing constructions of fractal surfaces over triangular domains, and secondly to connect the idea of fractal surfaces further with the theory of approximation. To this end, in the same spirit of the so-called (alpha )-fractal functions on intervals and hyperrectangles, we study a salient subclass of fractal surfaces, which provides a parameterized family of bivariate fractal functions corresponding to a fixed continuous function defined on a triangular domain. Some elementary properties of the single-valued (linear and nonlinear) and multi-valued fractal operators associated with the (alpha )-fractal function formalism of the bivariate fractal functions on a triangular domain are recorded. A fractal approximation process, that is a sequence of single-valued fractal operators converging strongly to the identity operator on ({mathcal {C}}(Delta , {mathbb {R}})), the space of all real-valued continuous functions defined on a triangular domain (Delta ), is obtained. An approximation class of fractal functions, referred to as the fractal polynomials, is hinted at. The notion of (alpha )-fractal function and associated single-valued fractal operator in conjunction with appropriate stability results for Schauder bases provide Schauder bases consisting of self-referential functions for ({mathcal {C}}(Delta , {mathbb {R}})).","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141425454","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

Identifying source term and initial value simultaneously for the time-fractional diffusion equation with Caputo-like hyper-Bessel operator 用卡普托类超贝塞尔算子同时识别时间分形扩散方程的源项和初值

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-06-17 DOI: 10.1007/s13540-024-00304-1

Fan Yang, Ying Cao, XiaoXiao Li

引用次数: 0

A high order predictor-corrector method with non-uniform meshes for fractional differential equations 分数微分方程的非均匀网格高阶预测器-校正器方法

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-06-12 DOI: 10.1007/s13540-024-00303-2

Farzaneh Mokhtarnezhadazar

引用次数: 0

Fractional difference inequalities for possible Lyapunov functions: a review 可能的 Lyapunov 函数的分数差分不等式：综述

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-06-12 DOI: 10.1007/s13540-024-00298-w

Yiheng Wei, Linlin Zhao, Xuan Zhao, Jinde Cao

引用次数: 0