On a Fractional Master Equation

A fractional order time-independent form of the wave equation or diffusion equation in two dimensions is obtained from the standard time-independent form of the wave equation or diffusion equation in two-dimensions by replacing the integer order partial derivatives by fractional Riesz-Feller derivative and Caputo derivative of order alpha, beta, 1 (SIC)(alpha) <= 2 and 1 > (SIC) <= 2 respectively. In this paper, we derive an analytic solution for the fractional time-independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented bymeans of theMittag-Leffler function. In all three cases, the solutions are represented also in terms of Fox's H-function.