  This paper deals with the investigation of the solution of an unified
fractional reaction-diffusion equation of distributed order associated with the
Caputo derivatives as the time-derivative and Riesz-Feller fractional
derivative as the space-derivative. The solution is derived by the application
of the joint Laplace and Fourier transforms in compact and closed form in terms
of the H-function. The results derived are of general nature and include the
results investigated earlier by other authors, notably by Mainardi et al.
[23,24], for the fundamental solution of the space-time fractional equation,
including Haubold et al. [13] and Saxena et al. [38] for fractional
reaction-diffusion equations. The advantage of using the 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 fractional diffusion, space-time fraction 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-function in compact forms. The convergence
conditions for the double series occurring in the solutions are investigated.
It is interesting to observe that the double series comes out to be a special
case of the Srivastava-Daoust hypergeometric function of two variables given in
the Appendix B of this paper.
