The Solution of Fokker Planck Equation Using Two Different Method: Aboodh Homotopy Perturbation Method and Aboodh Residuel Power Series Method

Résumé

The aim of this article is to address the objective of solving and analysing the time fractional form of a Fokker Planck equation using two methods which are noted for their efficiency, accuracy, easy of application and calculation, and flexibility, we employ the Aboodh Residual Power Series Method (ARPSM) and the Homotopy Perturbation Method (HPM). These methods are particularly suited for handling fractional differential equations and are known for their robustness in dealing with complex problems. The two proposed methods, the Aboodh Residual Power Series Method (ARPSM) and the Homotopy Perturbation Method (HPM), are highly effective mathematical techniques for studying more complicated nonlinear differential equations. These methods are capable of producing precise approximate solutions for intricate evolution equations, extending beyond the specific examined equations. By using the Caputo derivative, these methods provide a more accurate representation of fractional order processes, capturing the memory and hereditary properties inherent in many physical systems.