Further solutions of fractional reaction–diffusion equations in terms of the H-function

摘要

This paper is in continuation of our earlier paper in which we have derived the solution of a unified fractional reaction–diffusion equation associated with the Caputo derivative as the time-derivative and Riesz–Feller fractional derivative as the space-derivative. In this paper, we consider a unified reaction–diffusion equation with the Riemann–Liouville fractional derivative as the time-derivative and Riesz–Feller derivative as the space-derivative. 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 results derived are of general character and include the results investigated earlier in [7], [8]. The main result is given in the form of a theorem. A number of interesting special cases of the theorem are also given as corollaries.