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The object of this paper is to present a computable solution of a fractionalpartial differential equation associated with a Riemann-Liouville derivative offractional order as the time-derivative and Riesz-Feller fractional derivativeas the space derivative. The method followed in deriving the solution is thatof joint Laplace and Fourier transforms. The solution is derived in a closedand computable form in terms of the H-function. It provides an elegantextension of the results given earlier by Debnath, Chen et al., Haubold et al.,Mainardi et al., Saxena et al., and Pagnini et al. The results obtained arepresented in the form of four theorems. Some results associated with fractionalSchroeodinger equation and fractional diffusion-wave equation are also derivedas special cases of the findings.

Computable solutions of fractional partial differential equations related to reaction-diffusion systems