The approximate solutions of fractional gas dynamics equations by means of fractional natural decomposition method

Abstract

In this work, a new practical method, which is named by the Fractional Natural Decomposition Method (FNDM), is proposed to obtain the approximate analytical solutions of fractional gas dynamics equations. The FNDM is a mixture of the Natural Transform Method and the Adomian Decomposition Method. In this method, the fractional derivatives are considered as Caputo sense and the nonlinear terms are determined by virtue of Adomian polynomials. Some test examples are given to demonstrate the efficiency and accuracy of the FNDM.