Natural decomposition method and coupled systems of nonlinear fractional order partial differential equations

Abstract

In this article, we present a method known as the Natural decomposition transform method (NDTM). This method is a couple of Natural transform and Adomian decomposition method. By means of this new method, we successfully handle some coupled systems of nonlinear fractional-order partial differential equations (NFPDEs). We obtain the solutions in the form of series which rapidly converges to the exact solution. Two test examples are provided for the illustration of our method.