A fractional model of Navier–Stokes equation arising in unsteady flow of a viscous fluid

In this paper, we present a reliable algorithm based on the new homotopy perturbation transform method (HPTM) to solve a time-fractional Navier–Stokes equation in a tube. The fractional derivative is considered in the Caputo sense. By using an initial value, the explicit solution of the equation has been presented in a closed form and then its numerical solution has been represented graphically. The new homotopy perturbation transform method is a combined form of the Laplace transform method and the homotopy perturbation method. The results obtained by the proposed technique indicate that the approach is easy to implement and computationally very attractive.