Time-fractional radial diffusion in a sphere

被引：32
|
作者：
Povstenko, Yuriy [1 ]
机构：
[1] Jan Dlugosz Univ Czestochowa, Inst Math & Comp Sci, PL-42200 Czestochowa, Poland
来源：
NONLINEAR DYNAMICS | 2008年 / 53卷 / 1-2期
关键词：
non-Fickean diffusion; anomalous diffusion; diffusion-wave equation; fractional calculus; Mittag-Leffler functions;
D O I：
10.1007/s11071-007-9295-1
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
The radial diffusion in a sphere of radius R is described using time-fractional diffusion equation. The Caputo fractional derivative of the order 0 <alpha < 2 is used. The Laplace and finite sin-Fourier transforms are employed. The solution is written in terms of the Mittag-Leffler functions. For the first and second time-derivative terms, the obtained solutions reduce to the solutions of the ordinary diffusion and wave equations. Several examples of signaling, source and Cauchy problems are presented. Numerical results are illustrated graphically.
引用
收藏
页码：55 / 65
页数：11
相关论文
共 50 条
  • [21] Time-fractional diffusion equation for signal smoothing
    Li, Yuanlu
    Liu, Fawang
    Turner, Ian W.
    Li, Tao
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 326 : 108 - 116
  • [22] Time-fractional diffusion equation with ψ-Hilfer derivative
    Vieira, Nelson
    Rodrigues, M. Manuela
    Ferreira, Milton
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (06):
  • [23] Asymptotic analysis of time-fractional quantum diffusion
    Hislop, Peter D.
    Soccorsi, Eric
    APPLIED MATHEMATICS LETTERS, 2024, 152
  • [24] A backward problem for the time-fractional diffusion equation
    Al-Jamal, Mohammad F.
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (07) : 2466 - 2474
  • [25] Uniqueness of the potential in a time-fractional diffusion equation
    Jing, Xiaohua
    Peng, Jigen
    JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2023, 31 (04): : 467 - 477
  • [26] Symmetry classification of time-fractional diffusion equation
    Naeem, I.
    Khan, M. D.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 42 : 560 - 570
  • [27] A class of time-fractional diffusion equations with generalized fractional derivatives
    Alikhanov, Anatoly A.
    Huang, Chengming
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 414
  • [28] On the maximum principle for a time-fractional diffusion equation
    Yuri Luchko
    Masahiro Yamamoto
    Fractional Calculus and Applied Analysis, 2017, 20 : 1131 - 1145
  • [29] NUMERICAL APPROXIMATION OF STOCHASTIC TIME-FRACTIONAL DIFFUSION
    Jin, Bangti
    Yan, Yubin
    Zhou, Zhi
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2019, 53 (04): : 1245 - 1268
  • [30] REGULARITY OF SOLUTIONS TO A TIME-FRACTIONAL DIFFUSION EQUATION
    McLean, William
    ANZIAM JOURNAL, 2010, 52 (02): : 123 - 138
12345