Solution of Time-Fractional Navier-Stokes Equation by Using Homotopy Analysis Method

The homotopy analysis method (HAM) is used to obtain an approximate solution of the nonlinear time fractional Navier-Stokes equation by introducing the fractional derivative in the caputos sense. Convergence of the solution and effects for the method are discussed within comparing the obtained results with exact solution of the corresponding nonlinear problem, which indicated that the proposed method is very effective and simple. The HAM contains a certain auxiliary parameter $h$ which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. It also suggests that both the homotopy perturbation method (HPM), Adomian decomposition method (ADM) and variational iteration method (VIM) are special cases of the HAM.