Abstract
In this paper, we consider linear and non-linear space-time fractional reaction-diffusion equations (STFRDE) on a finite domain. The equations are obtained from standard reaction-diffusion equations by replacing a second-order space derivative by a fractional derivative of order beta is an element of (1, 2], and a first-order time derivative by a fractional derivative of order alpha is an element of (0, 1]. We use the Adomian decomposition method to construct explicit solutions of the linear and non-linear STFRDE. Finally, some examples are given. Copyright (C) 2007 John Wiley & Sons, Ltd.