A NEW APPROACH OF GENERALIZED TOUCHARD POLYNOMIALS TO SOLVE FRACTIONAL FOKKER-PLANCK EQUATIONS WITH VARIABLE COEFFICIENTS

This paper presents a novel method for solving fractional Fokker-Planck equations with variable coefficients (FFPE-VC) using generalized Touchard polynomials (GTPs). The method involves using GTPs and operational matrices of classical and fractional derivatives for GTPs to obtain a series solution for the FFPE-VC model. The Lagrange multipliers method is used to reduce the proposed problem to a system of algebraic equations, which is then solved using Matlab and Maple software. The paper discusses the convergence analysis and presents several examples to demonstrate the accuracy and effectiveness of the proposed method. The method is applicable to similar problems in the field of engineering and physics.