A Reliable Decomposition Method for Fractional-Order Fokker–Planck Equation

This study analytically investigates the fractional Fokker–Planck equations (F-FPEs) by employing the Sumudu decomposition method (SDM). This method combines the strengths of the Sumudu transform and the Adomian decomposition method (ADM) to effectively handle the nonlocality and memory characteristics inherent in governing fractional differential equations. Certainly, upon systematically applying the technique, the resulting approximate analytical solutions are acquired recurrently. The accuracy and performance of the method are further validated through comparisons with the traditional ADM and the homotopy perturbation Sumudu transform method. Numerical results and graphical illustrations confirm that SDM yields highly accurate solutions that closely match the exact solutions. All symbolic computations and recursive schemes were implemented using Maple software. The findings suggest that SDM is a reliable and efficient technique for handling dissimilar classes of fractional-order nonlinear differential equations.