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

被引：0

作者：

Idczak, Dariusz ^{[1
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2024年 / 27卷 / 06期

关键词：

Functions of two variables; Riemann-Liouville derivative; Weak derivative; Fractional absolute continuity; Fractional Sobolev type spaces; FUNDAMENTAL LEMMA; ORDER;

D O I：

10.1007/s13540-024-00344-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2892 / 2947

页数：56

共 50 条

[1] Fractional Sobolev Spaces via Riemann-Liouville Derivatives
Idczak, Dariusz
Walczak, StanisBaw
JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,
[2] Riemann-Liouville derivatives of abstract functions and Sobolev spaces
Idczak, Dariusz
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2022, 25 (03) : 1260 - 1293
[3] Riemann-Liouville derivatives of abstract functions and Sobolev spaces
Dariusz Idczak
Fractional Calculus and Applied Analysis, 2022, 25 : 1260 - 1293
[4] A NOTE ON RIEMANN-LIOUVILLE FRACTIONAL SOBOLEV SPACES
Carbotti, Alessandro
Comi, Giovanni E.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (01) : 17 - 54
[5] Bilateral Riemann-Liouville Fractional Sobolev spaces
Leaci, A.
Tomarelli, F.
NOTE DI MATEMATICA, 2021, 41 (02): : 61 - 83
[6] Riemann-Liouville Fractional Sobolev and Bounded Variation Spaces
Leaci, Antonio
Tomarelli, Franco
AXIOMS, 2022, 11 (01)
[7] Opial type inequalities involving Riemann-Liouville fractional derivatives of two functions with applications
Anastassiou, George A.
MATHEMATICAL AND COMPUTER MODELLING, 2008, 48 (3-4) : 344 - 374
[8] Liouville and Riemann-Liouville fractional derivatives via contour integrals
Tohru Morita
Ken-ichi Sato
Fractional Calculus and Applied Analysis, 2013, 16 : 630 - 653
[9] Liouville and Riemann-Liouville fractional derivatives via contour integrals
Morita, Tohru
Sato, Ken-ichi
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (03) : 630 - 653
[10] Approximation with Riemann-Liouville fractional derivatives
Anastassiou, George A.
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2019, 64 (03): : 357 - 365

← 1 2 3 4 5 →