  This paper deals with the investigation of the computational solutions of an
unified fractional reaction-diffusion equation, which is obtained from the
standard diffusion equation by replacing the time derivative of first order by
the generalized fractional time-derivative defined by Hilfer (2000), the space
derivative of second order by the Riesz-Feller fractional derivative and adding
the function phi(x,t) which is a nonlinear function overning reaction. The
solution is derived by the application of the Laplace and Fourier transforms in
a compact and closed form in terms of the H-function. The main result obtained
in this paper provides an elegant extension of the fundamental solution for the
space-time fractional diffusion equation obtained earlier by Mainardi et al.
(2001, 2005) and a result very recently given by Tomovski et al. (2011).
Computational representation of the fundamental solution is also obtained
explicitly. Fractional order moments of the distribution are deduced. At the
end, mild extensions of the derived results associated with a finite number of
Riesz-Feller space fractional derivatives are also discussed.
