The Multistage Homotopy-Perturbation Method: A Powerful Scheme for Handling a Fractional Lorenz System

In this chapter, the multistage homotopy perturbation method (MHPM) is used to give analytical solutions of the time fractional Lorenz system in Caputo sense. This method is a modification of the standard homotopy perturbation method (HPM) which yields an analytical solution in terms of a convergent infinite power series with easily computable terms. Some numerical comparisons between the (MHPM) and (HPM) with the 4th order Runge-Kutta method (RK4) is presented. Moreover, we reinforce our results by constructing the residual error for the solution. It is concluded that the (MHPM) is reliable and effective tool in finding analytical solutions and it is very easy to construct an accurate approximate solution for the fractional Lorenz system.