Optimal Homotopy Anaylsis Method for Nonlinear Partial Fractional Differential Fisher's Equation

In this article, we use the fractional complex transform and the optimal homotopy analysis method (OHAM) to find the analytical approximate solutions for time-space nonlinear partial fractional Fisher's equation. Fractional complex transformation is proposed to convert time-space nonlinear partial fractional differential Fisher's equation to nonlinear partial differential equations. Also, we use the OHAM to find the numerical solution for nonlinear PFDEs. This optimal approach has general meaning and can be used to get the fast convergent series solutions of the different type of nonlinear partial fractional differential equations. The results reveal that this method is very effective and powerfull to obtain the approximate solutions. The OHAM contains a certain auxiliary parameter h which provides us a simple way to adjust and control the convergence region to the series solution.