Investigation of two scale fractional partial differential equations: An Analytical Approach

Abstract

In this study, Reduced Differential Transform Method (RDTM) is implemented for analyzing approximate analytical solution of two scale fractional partial differential equations subject to appropriate initial conditions. The proposed technique is an effective and powerful approximate analytical tool to obtain the solutions of many linear and nonlinear fractional partial differential equations that appears in numerous science, engineering, and industrial applications. This method has an advantage of finding an analytical approximate solution in terms of convergent power series with a smaller number of terms that can be calculated easily. In order to determine the validity and efficacy of the method, two test problems are given. The results obtained are correlated to the classical order and compared with the solutions obtained by Sumudu decomposition method. Additionally, the results indicate that the suggested approach is competent to study the fractional behavior of many other differential equations