new approaches for solving caputo time-fractional nonlinear system of equations describing the unsteady flow of a polytropic gas

The main object of this manuscript is to achieve the solutions of a time-fractional nonlinear system of equations describing the unsteady flow of a polytropic gas using two different approaches based on the combination of new general integral transform in the sense of caputo fractional derivative and homotopy perturbation method and variational iteration method, respectively. the solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. numerical results reveal that the proposed approaches are very effective and simple to obtain approximate and analytical solutions for nonlinear systems of fractional partial differential equations.