Comparative semi-analytical solutions of Caputo time-fractional Fokker–Planck equations via Laplace transform–based decomposition and iterative methods

In this study, the Laplace Adomian Decomposition Method (LADM) and the Laplace Variational Iteration Method (LVIM) are employed to obtain approximate analytical solutions for both linear and nonlinear time-fractional Fokker-Planck equations (TFFPEs). These methods combine the Laplace transform with the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM), respectively. Fractional derivatives are considered in the Caputo sense. The proposed approaches are straightforward to implement and yield solutions without requiring linearization, discretization, or perturbation. Several examples are solved and presented both graphically and numerically to illustrate the accuracy and stability of the methods. A comparison with the exact solution for the classical case confirms that the approximate solutions are in excellent agreement with the exact results. Further comparisons with other methods indicate that the proposed approaches provide improved accuracy while reducing computational effort. All tabular and graphical results are generated using Python. Additionally, the stability and convergence of the proposed methods for TFFPEs are analyzed.