Nonlinear time-fractional partial differential equations, especially nonlinear time-fractional Gas dynamic equations, can be resolved by applying the Optimal Homotopy Asymptotic Method (OHAM) and the Least Square Residual Power Series Method (LSRPSM). A Fractional-order derivative that has numerical values in the closed interval [0, 1] is being employed in the Caputo meaning. These approaches are compared based on their computing complexity, convergence rate, and approximation error. The present study demonstrates that when these techniques are assigned to nonlinear differential equations of fractional order, they exhibit differing convergence rates and approximation errors. Using the Matlab software, perform numerical computations and graphics for fractional gas differential equations. The results of this comparison are compared to the exact solution to demonstrate how much more efficient and precise our methods are at solving nonlinear differential equations. In comparison to (OHAM), the research's findings demonstrate the validity and efficiency of the series solution utilizing (LSRPSM), showing the importance of these methods in the study of fractional differential equations.