Analytic Solutions of (N+1) Dimensional Time Fractional Diffusion Equations by Fractional Iterative Laplace Transform Method (Global Journal of Science Frontier Research, 2018)
In this paper, the author has been examined how to obtain solutions of (n+1) dimensional time fractional diffusion equations with initial conditions in the form of infinite fractional power series, in terms of Mittage Lefler function of one parameter and exact form by the use of iterative fractional Laplace transform method (IFLTM). The basic idea of the IFLTM was developed successfully. To see its effectiveness and applicability, three test examples were presented. The closed solutions in the form of infinite fractional power series and in terms of Mittag-Leffler functions in one parameter, which rapidly converge to exact solutions, were successfully derived analytically by the use of iterative fractional Laplace transform method (IFLTM). Thus, the results show that the iterative fractional Laplace transform method works successfully in solving (n+1) dimensional time fractional diffusion equations in a direct way without using linearization, perturbation, discretization or restrictive assumptions, and hence it can be extended to other fractional differential equations.
Keywords: (n 1) dimensional time fractional diffusion equations with initial conditions; caputo fractional derivatives; mittag-leffler function; iterative fract