Numerical solution of the nonlinear fractional partial differential equations

In this article, we applied the optimal auxiliary function method, which is a newly developed semi-numerical method widely used for complicated nonlinear partial differential equations in many complicated physical problems. This method is implemented for a nonlinear time-fractional hyperbolic equation, a nonlinear time-fractional Fisher's equation, and a nonlinear fractional partial differential equation with some initial conditions. The method yields a rapidly convergent series solution, which is then validated by comparison with exact results. It shows the method's exactness, accuracy, and convergence in graphical analysis. The study results show the optimal auxiliary function method is applicable in an easy way, holds concise computational work, and quickly converges to a particular result.