Homotopy Analysis Transform Method for Time-Space Fractional Gas Dynamics Equation

Homotopy Analysis Transform Method (HATM) is applied to tackle time-space fractional Gas dynamics equation. The proposed HATM is an elegant coupling of homotopy analysis method (HAM) and Laplace transform. The method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive. Numerical results coupled with graphical representation explicitly reveal the complete reliability of the proposed algorithm.