Computable Solutions of Fractional Reaction-Diffusion Equations Associated with Generalized Riemann-Liouville Fractional Derivatives of Fractional Order

Abstract: This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative is derived. In the present paper, computable solutions of distributed order fractional reaction-diffusion equations associated with generalized Riemann-Liouville derivatives of fractional orders as the time-derivative and Riesz-Feller fractional derivative as the space derivative are investigated. The solutions of the fractional reaction-diffusion equations of fractional orders are obtained in this paper. The method followed in deriving the solutions is that of joint Laplace and Fourier transforms. The solutions obtained are in a closed and computable form in terms of the familiar generalized Mittag-Leffler functions. They provide elegant extensions of the results given in the literature.