Semi-Analytic Solution of Fractional Fokker-Planck and Fornburg-Whitham Equations Using a Unique Technique

Abstract

In this work, a new hybrid semi-analytical method is presented, merging the Kamal Transform and the Homotopy Perturbation Method (HPM), for solving fractional differential equations (FDEs) involving the Caputo derivative. The method is used to solve complex systems such as the Fokker-Planck and Fornberg-Whitham equations. This method beats classical iterative techniques in both computational efforts and simplicity. Numerous tables and graphics display the numerical results, establishing the method's accuracy by reference to the residual power series method and exact solutions. Our results illustrate the strength and the precision of this technique to be very efficient with a minor cost against numerical solution techniques for fractional partial differential equations.