Numerical computation of nonlinear shock wave equation of fractional order

The main aim of the present paper was to present a user friendly approach based on homotopy analysis transform method to solve a time-fractional nonlinear shock wave equation arising in the flow of gases. The proposed technique presents a procedure of constructing the set of base functions and gives the high-order deformation equations in a simple form. The auxiliary parameter ℏ in the homotopy analysis transform method solutions has provided a convenient way of controlling the convergence region of series solutions. The method is not limited to the small parameter, such as in the classical perturbation method. The technique 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 approach indicate that the approach is easy to implement and computationally very attractive.