analytical approximate solution for nonlinear time-space fractional fornberg-whitham equation by fractional complex transform

In this article, fractional complex transform with optimal homotopy analysis method (OHAM) is used to obtain numerical and analytical solutions for the nonlinear time-space fractional Fornberg-Whitham. Fractional complex transform is proposed to convert time-space fractional Fornberg-Whitham equation to the nonlinear ordinary differential equations and then applied OHAM to the new obtained equations. This optimal approach has general meaning and can be used to get fast convergent series solutions of the different type of nonlinear fractional differential equation. The results reveal that the method is very effective, simple and the OHAM contains a certain auxiliary parameter $h$ which provides us with a simple way to adjust and control the convergence region of convergence of the series solution.