Analytical solution of fractional Navier-Stokes equation by using modified Laplace decomposition method

The aim of this article is to introduce a new analytical and approximate technique to obtain the solution of time-fractional Navier-Stokes equation in a tube. This proposed technique is the coupling of Adomian decomposition method (ADM) and Laplace transform method (LTM). We have consider the unsteady flow of a viscous fluid in a tube in which, besides time as one of the dependent variable, the velocity field is a function of only one space coordinate. A good agreement between the obtained solutions and some well-known results has been demonstrated. It is shown that the proposed method robust, efficient, and easy to implement for linear and nonlinear problems arising in science and engineering.