The fundamental solutions for the fractional diffusion-wave equation

被引：519

作者：

Mainardi, F

机构：

[1] Department of Physics, University of Bologna, I-40126 Bologna

来源：

APPLIED MATHEMATICS LETTERS | 1996年 / 9卷 / 06期

关键词：

fractional derivative; diffusion equation; wave equation; green function; Wright function;

D O I：

10.1016/0893-9659(96)00089-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The time fractional diffusion-wave equation is obtained from the classical diffusion or wave equation by replacing the first- or second-order time derivative by a fractional derivative of order 2 beta with 0 < beta less than or equal to 1/2 or 1/2 < beta less than or equal to 1, respectively. Using the method of the Laplace transform, it is shown that the fundamental solutions of the basic Cauchy and Signalling problems can be expressed in terms of an auxiliary function M(z; beta), where z = \x\/t(beta) is the similarity variable. Such function is proved to be an entire function of Wright type.

引用

页码：23 / 28

页数：6