  This paper deals with the investigation of the solution of an unified
fractional reaction-diffusion equation associated with the Caputo derivative as
the time-derivative and Riesz-Feller fractional derivative as the
space-derivative. The solution is derived by the application of the Laplace and
Fourier transforms in closed form in terms of the H-function. The results
derived are of general nature and include the results investigated earlier by
many authors, notably by Mainardi et al. (2001, 2005) for the fundamental
solution of the space-time fractional diffusion equation, and Saxena et al.
(2006a, b) for fractional reaction- diffusion equations. The advantage of using
Riesz-Feller derivative lies in the fact that the solution of the fractional
reaction-diffusion equation containing this derivative includes the fundamental
solution for space-time fractional diffusion, which itself is a generalization
of neutral fractional diffusion, space-fractional diffusion, and
time-fractional diffusion. These specialized types of diffusion can be
interpreted as spatial probability density functions evolving in time and are
expressible in terms of the H-functions in compact form.
