Analytical Solution of Fractional Order Diffusion Equations Using Iterative Laplace Transform Method

In this present article, by using the Iterative Laplace Transform Method (ILTM), the diffusion equation of fractional order is solved. The ILTM, which works as a combination of two methods, the iterative method and the other is the Laplace transform method, is applied to several diffusion equations to obtain analytical solutions. The proposed method gives the closed-form of series solutions in terms of the Mittag-Leffler function, which is a queen of functions in fractional calculus. The main aim of this work is to present a simple but reliable algorithm for the solution of diffusion equations of the multi-dimensional type, which clearly describes the materials of density dynamics in the diffusion process. The results obtained by using the ILTM approach indicate that this approach is attractive computationally and implemented easily. Due to its straightforward approach and comfortable way of solving problems, the ILTM can be utilized to solve nonlinear fractional problems in various applied and engineering sciences.