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.
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页码：55 / 65
页数：11
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