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
收藏
页码：2892 / 2947
页数：56
相关论文
共 50 条
  • [31] On a Riemann-Liouville Type Implicit Coupled System via Generalized Boundary Conditions
    Riaz, Usman
    Zada, Akbar
    Ali, Zeeshan
    Popa, Ioan-Lucian
    Rezapour, Shahram
    Etemad, Sina
    MATHEMATICS, 2021, 9 (11)
  • [32] Analytical Solution of Linear Fractional Systems with Variable Coefficients Involving Riemann-Liouville and Caputo Derivatives
    Matychyn, Ivan
    SYMMETRY-BASEL, 2019, 11 (11):
  • [33] LIPSCHITZ STABILITY FOR IMPULSIVE RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL EQUATIONS
    Bohner, Martin
    Hristova, Snezhana
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2024, 48 (05): : 723 - 745
  • [34] Stability analysis of fractional differential system with Riemann-Liouville derivative
    Qian, Deliang
    Li, Changpin
    Agarwal, Ravi P.
    Wong, Patricia J. Y.
    MATHEMATICAL AND COMPUTER MODELLING, 2010, 52 (5-6) : 862 - 874
  • [35] Nonlocal Riemann-Liouville fractional evolution inclusions in Banach space
    Bilal, Shamas
    Donchev, Tzanko
    Kitanov, Nikolay
    Javaid, Nasir
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (08)
  • [36] Abundant new exact solutions to the fractional nonlinear evolution equation via Riemann-Liouville derivative
    Uddin, M. Hafiz
    Khatun, M. Ayesha
    Arefin, Mohammad Asif
    Akbar, M. Ali
    ALEXANDRIA ENGINEERING JOURNAL, 2021, 60 (06) : 5183 - 5191
  • [37] Solvability of Anti-periodic BVPs for Impulsive Fractional Differential Systems Involving Caputo and Riemann-Liouville Fractional Derivatives
    Liu, Yuji
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2018, 19 (02) : 125 - 152
  • [38] VARIATIONAL ITERATION METHOD FOR SUBDIFFUSION EQUATIONS WITH THE RIEMANN-LIOUVILLE DERIVATIVES
    Wei, Ming-Bo
    Wu, Guo-Cheng
    HEAT TRANSFER RESEARCH, 2013, 44 (05) : 409 - 415
  • [39] GLOBAL ATTRACTIVITY FOR SOME CLASSES OF RIEMANN-LIOUVILLE FRACTIONAL DIFFERENTIAL SYSTEMS
    Tuan, H. T.
    Czornik, Adam
    Nieto, Juan J.
    Niezabitowski, Michal
    JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2019, 31 (02) : 265 - 282
  • [40] On asymptotics of solutions for superdiffusion and subdiffusion equations with the Riemann-Liouville fractional derivative
    Li, Zhiqiang
    Fan, Yanzhe
    AIMS MATHEMATICS, 2023, 8 (08): : 19210 - 19239
12345