Fractional differential equations and its solutions using the Laplace Variational Iteration Method

Abstract

In this paper, we discuss fractional differential equations, including the Fokker-Planck equation and fractional diffusion differential equations, which are closely related to chemistry and engineering. To solve these equations, we employ the Laplace Variational Iteration Method (LVIM), which combines the Laplace transform with He’s Variational Iteration Method. To demonstrate the efficiency and validity of LVIM, we consider two 1-D Fokker-Planck equations and three fractional diffusion equations in 1-D, 2-D, and 3-D. We solve these equations using LVIM, and the results are presented analytically in tables and graphically using MATLAB for different values of the fractional order and these results are then compared with those obtained by existing methods. The solutions obtain as infinite series, and for certain values of the fractional order, they are found to be similar to the exact results.

GANIT J. Bangladesh Math. Soc. 45.2 (2025) 031–044