A reliable method for the space-time fractional Burgers and time-fractional Cahn-Allen equations via the FRDTM

Abstract

Abstract We propose a new method called the fractional reduced differential transform method (FRDTM) to solve nonlinear fractional partial differential equations such as the space-time fractional Burgers equations and the time-fractional Cahn-Allen equation. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers and Cahn-Allen equations to show the nature of solutions as the fractional derivative parameter is changed. The results prove that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.

Keywords

• fractional reduced differential transform method
• Caputo fractional derivative
• Burgers equations
• Cahn-Allen equation