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

This article’s objective is to solve and analyze the time fractional form of a Fokker-Planck equation using two techniques that are renowned for their effectiveness, precision, ease of use and computation, and adaptability: the Homotopy Perturbation Method and the Aboodh Residual Power Series Method. These techniques are well-known for their resilience when solving complicated issues, and they are especially well-suited for handling fractional differential equations. For the analysis of more complex nonlinear differential equations, the two suggested approaches—the Homotopy Perturbation Method and the Aboodh Residual Power Series Method—are very successful mathematical strategies. Beyond the particular equations under study, these techniques can yield accurate approximations of solutions to complex evolution equations. These techniques capture the memory and heredity characteristics present in many physical systems and offer a more realistic depiction of fractional order processes by employing the Caputo derivative.