On the solutions of non-linear time-fractional gas dynamic equations: An analytical approach

Abstract

We consider non-linear homogeneous and non-homogeneous gas dynamic equations of time-fractional type in this paper. The approximate solutions of these equations are calculated in the form of series obtained by q-Homotopy Analysis Method (q-HAM). Exact solution is obtained for timefractional homogeneous case while for the case of time-fractional non-homogeneous, exact solution is possible for special case. This is due to the ability to control the auxiliary parameter h and the fraction factor present in this method. The presence of fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made with several other analytical methods.