Semi analytical scheme for the presentation of solution to Fractional Fokker–Planck Equation

Abstract

In this work, we have also proposed new semi analytical scheme combining least-squares and asymptotic homotopy perturbation methods AHPM for the solution of Fractional Fokker–Planck Equation (FFPE). The Caputo version of derivative is used. The finding of this work is fast convergence of the AHPM to the solutions of linear and nonlinear applied problems. AHPM is a modified form of the HPM and is particularly useful for solving problems with small or large parameters. This can be seen as a clear advantage of this new semi analytical method over existing methods because its implementation and the calculation involved in it are much simpler and easier. The proposed method solved the problems without using Ji-Huan He and Adomian polynomials. Numerical solutions obtained in this way show that this approach is simple and computationally very attractive. An error estimate for the solution is also provided. Approximate solutions of AHPM are tabulated and graphically displayed to show that AHPM is effective and accurate.

Keywords

• Homotopy method
• Numerical analysis
• Caputo derivative
• Fractional Fokker–Planck equation