The space-time fractional diffusion equation with Caputo derivatives

被引：43
作者：
Huang F. [1 ,3 ]
Liu F. [1 ,2 ]
机构：
[1] Department of Mathematical Sciences, Xiamen University
[2] School of Mathematical Sciences, Queensland University of Technology
[3] School of Mathematical Sciences, South China University of Technology
来源：
Journal of Applied Mathematics and Computing | 2005年 / 19卷 / 1-2期
关键词：
Caputo derivative; Fourier transform; Fractional diffusion equation; Green function; Laplace transform; Mittag-Leffler function; Stable probability distributions; Time-space;
D O I：
10.1007/BF02935797
中图分类号：
学科分类号：
摘要：
We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order β ∈ (0,2] and the first-order time derivative with Caputo derivative of order α ∈ (0,1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation. © 2005 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.
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收藏
页码：179 / 190
页数：11
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