Fractional Calculus and Applied Analysis最新文献_第10页

Analysis of a class of completely non-local elliptic diffusion operators 一类完全非局部椭圆扩散算子的分析

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-29 DOI: 10.1007/s13540-024-00254-8

{"title":"Analysis of a class of completely non-local elliptic diffusion operators","authors":"","doi":"10.1007/s13540-024-00254-8","DOIUrl":"https://doi.org/10.1007/s13540-024-00254-8","url":null,"abstract":"<h3>Abstract</h3> This work explores the possibility of developing the analog of some classic results from elliptic PDEs for a class of fractional ODEs involving the composition of both left- and right-sided Riemann-Liouville (R-L) fractional derivatives, ({D^alpha _{a+}}{D^beta _{b-}}) , (1<alpha +beta <2) . Compared to one-sided non-local R-L derivatives, these composite operators are completely non-local, which means that the evaluation of ({D^alpha _{a+}}{D^beta _{b-}}u(x)) at a point x will have to retrieve the information not only to the left of x all the way to the left boundary but also to the right up to the right boundary, simultaneously. Therefore, only limited tools can be applied to such a situation, which is the most challenging part of the work. To overcome this, we do the analysis from a non-traditional perspective and eventually establish elliptic-type results, including Hopf’s Lemma and maximum principles. As (alpha rightarrow 1^-) or (alpha ,beta rightarrow 1^-) , those operators reduce to the one-sided fractional diffusion operator and the classic diffusion operator, respectively. For these reasons, we still refer to them as “elliptic diffusion operators", however, without any physical interpretation.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139994409","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

Optimal control of fractional non-autonomous evolution inclusions with Clarke subdifferential 具有克拉克次微分的分数非自治演化夹杂物的优化控制

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-27 DOI: 10.1007/s13540-024-00258-4

Xuemei Li, Xinge Liu, Fengzhen Long

引用次数: 0

Discrete convolution operators and equations 离散卷积算子和方程

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-27 DOI: 10.1007/s13540-024-00253-9

引用次数: 0

Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process 罗森布拉特过程驱动的阶（1，2）分式随机半变量不等式的近似最优控制

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-27 DOI: 10.1007/s13540-024-00257-5

Zuomao Yan

引用次数: 0

Schrödinger-Maxwell equations driven by mixed local-nonlocal operators 由混合局部-非局部算子驱动的薛定谔-麦克斯韦方程

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-26 DOI: 10.1007/s13540-024-00251-x

引用次数: 0

A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability 带亚扩散可能阻尼项的时分超扩散类波方程：拟合性和米塔格-勒弗勒稳定性

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-26 DOI: 10.1007/s13540-024-00249-5

引用次数: 0

The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II Bochner-Lebesgue 空间中的黎曼-刘维尔分数积分 II

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-26 DOI: 10.1007/s13540-024-00255-7

引用次数: 0

Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators Orlicz-Lorentz-Karamata Hardy martingale 空间：不等式和分数积分算子

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-23 DOI: 10.1007/s13540-024-00259-3

Zhiwei Hao, Libo Li, Long Long, Ferenc Weisz

{"title":"Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators","authors":"Zhiwei Hao, Libo Li, Long Long, Ferenc Weisz","doi":"10.1007/s13540-024-00259-3","DOIUrl":"https://doi.org/10.1007/s13540-024-00259-3","url":null,"abstract":"Let (0<qle infty ), b be a slowly varying function and ( Phi : [0,infty ) longrightarrow [0,infty ) ) be an increasing function with (Phi (0)=0) and (lim limits _{r rightarrow infty }Phi (r)=infty ). In this paper, we introduce a new class of function spaces (L_{Phi ,q,b}) which unify and generalize the Lorentz-Karamata spaces with (Phi (t)=t^p) and the Orlicz-Lorentz spaces with (bequiv 1). Based on the new spaces, we introduce five new Hardy spaces containing martingales, the so-called Orlicz-Lorentz-Karamata Hardy martingale spaces and then develop a theory of these martingale Hardy spaces. To be precise, we first investigate several properties of Orlicz-Lorentz-Karamata spaces and then present Doob’s maximal inequalities by using Hardy’s inequalities. The characterization of these Hardy martingale spaces are constructed via the atomic decompositions. As applications of the atomic decompositions, martingale inequalities and the relation of the different martingale Hardy spaces are presented. The dual theorems and a new John-Nirenberg type inequality for the new framework are also established. Moreover, we study the boundedness of fractional integral operators on Orlicz-Lorentz-Karamata Hardy martingale spaces. The results obtained here generalize the previous results for Lorentz-Karamata Hardy martingale spaces as well as for Orlicz-Lorentz Hardy martingales spaces. Especially, we remove the condition that b is non-decreasing as in [38, 39] and the condition (q_{Phi ^{-1}}<1/q) in [24], respectively.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139957157","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

Operational matrix based numerical scheme for the solution of time fractional diffusion equations 基于运算矩阵的时间分数扩散方程数值求解方案

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-23 DOI: 10.1007/s13540-024-00252-w

S. Poojitha, Ashish Awasthi

引用次数: 0

On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications 各向异性变指数索波列夫空间的集中-紧凑性原理及其应用

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-02-22 DOI: 10.1007/s13540-024-00246-8

Nabil Chems Eddine, Maria Alessandra Ragusa, Dušan D. Repovš

引用次数: 0