Numerical solutions of fractional Fokker-Planck equation with hybrid method of solution

Olubanwo, Oludapo Omotola; Idowu, Sunday Senayon; Adepoju, Julius Temitayo; Ajani, Abiodun Sufiat

doi:10.22060/ajmc.2024.23176.1238

Numerical solutions of fractional Fokker-Planck equation with hybrid method of solution

Document Type : Original Article

Authors

Oludapo Omotola Olubanwo

Sunday Senayon Idowu

Julius Temitayo Adepoju

Abiodun Sufiat Ajani

Department of Mathematical Sciences, Faculty of Science, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria

10.22060/ajmc.2024.23176.1238

Abstract

The work employs a numerical method for the solution of Fractional Fokker-Planck Equation (FFPE) using the Homotopy Perturbation and Aboodh Transform Method (HPATM). Fractional derivatives issues are successfully solved using the hybrid approach, which yields rapidly convergent solutions. By resolving two cases and contrasting estimated outcomes with exact solutions for various fractional orders, the correctness of the technique was proven. The accuracy of the technique is demonstrated by the good match between the precise and approximation solutions at $\alpha=1$. The findings indicate that fractional differential equations may be solved with a strong and dependable approach using HPATM, which can also be used to describe anomalous diffusion and other intricate physical phenomena.

Keywords

Fokker-Planck equation

FPDE

HPM

Integral transforms

Subjects