Fractional Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-10-07 DOI:10.1007/s13540-024-00344-7

Dariusz Idczak

引用次数: 0

Abstract

We introduce and study the spaces of fractionally absolutely continuous functions of two variables of any order and the fractional Sobolev type spaces of functions of two variables. Our approach is based on the Riemann-Liouville fractional integrals and derivatives. We investigate relations between these spaces as well as between the Riemann-Liouville and weak derivatives.

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通过黎曼-刘维尔导数计算两变量函数的分数索波列夫类型空间

我们介绍并研究任意阶分数绝对连续的两变量函数空间以及分数索波列夫类型的两变量函数空间。我们的方法基于黎曼-李欧维尔分数积分和导数。我们研究了这些空间之间的关系，以及黎曼-李欧维尔和弱导数之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.