Application of the Homotopy Analysis Method to Fractional Order Gas Dynamics Equation

In this paper, an analytical technique, namely the homotopy analysis method (HAM) is applied to obtain an approximate analytical solution of the nonlinear fractional partial di¤er- ential equation gas dynamics equation. Convergence of the solution and e¤ects for the method are discussed. The results reveal that the proposed method is very e¤ective and simple. It also suggests that both the homotopy perturbation method (HPM), Adomian decomposition method (ADM) and variational iteration method (VIM) are special cases of the HAM. The HAM contains a certain auxiliary parameter h which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution.