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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 time- fractional homogeneous case while for the case of time-fractional non-homo- geneous, 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 exist- ing analytical methods for non-linear differential equations. Comparisons are made with several other analytical methods.

ON THE SOLUTIONS OF NON-LINEAR TIME-FRACTIONAL GAS DYNAMIC EQUATIONS: AN ANALYTICAL APPROACH