Analytic Solutions of Initial Value Problems of Homogeneous Time Fractional Heat-Like Equations Using the Reduced Differential Transform Method

Abstract

The main purpose of this study was to develop a scheme to find analytic solutions of multidimensional homogeneous time fractional heat like equations under initial conditions by using reduced differential transform method. Analytic solutions based on the iteration technique were proposed (designed) to solve the homogeneous time-fractional heat-like equations in ndimensions using Reduced Differential Transform Method subjected to the appropriate initial condition. The Reduced Differential Transform Method procedures in one, two, three and more than three dimensions were developed and introduced to obtain the analytic solutions of multidimensional homogeneous time fractional heat-like equations. To see the effectiveness and applicability of the newly introduced procedures of the Reduced Differential Transform Method to obtain analytic solutions of initial value problems of homogeneous time fractional heat-like equations in n-dimensional space (n), four test examples were presented. The results show that Reduced Differential Transform Method is successfully implemented to obtain analytic solutions of multi-dimensional homogeneous time fractional linear heat-like equations. Therefore, it can be concluded that the proposed method can be extended to other fractional partial differential equations which can arise in physics and engineering.