Computational analysis of a normalized time-fractional Fokker-Planck equation

We propose a normalized time-fractional Fokker-Planck equation (TFFPE). A finite ence method is used to develop a computational method for solving the equation, system's dynamics are investigated through computational simulations. The proposed demonstrates accuracy and efficiency in approximating analytical solutions. Numerical validate the method's effectiveness and highlight the impact of various fractional the dynamics of the normalized time-fractional Fokker-Planck equation. The numerical emphasize the significant impact of different fractional orders on the temporal evolution the system. Specifically, the computational results demonstrate how varying the order influences the diffusion process, with lower orders exhibiting stronger memory and slower diffusion, while higher orders lead to faster propagation and a transition classical diffusion behavior. This work contributes to the understanding of fractional and provides a robust tool for simulating time-fractional systems.