A comparative analysis of the variational iteration and the Adomian decomposition methods for solving fractional-order partial derivatives with weakly singular kernel

Abstract

This paper examines the comparative methods of obtaining approximate solutions to fractional order partial derivatives using the variational iteration method (VIM) and the Adomian decomposition method (ADM). By appropriately imposing the initial conditions, an integral equation in the form of a correction functional is constructed using the general Lagrange multiplier. It is generally believed that the iteration method gives the solutions in the form of convergent series giving it some advantage over other methods of numerical solutions since it requires no linearization, discretization or perturbations. Numerical simulations are also employed to obtained the graphical solutions of the methods, and comparison really showed that the VIM gives a better approximate solution compared to ADM.