Convergence Analysis of Variational Iteration Method for Caputo Fractional Differential Equations

Abstract

Abstract. In this paper, the variational iteration method is applied to solve initial value problems of Caputo fractional differential equations. The convergence of the variational iteration method for solving the initial value problems of the kind of equation has been proved. The numerical examples show the efficiency of the variational iteration method for solving the initial value problems of the kind of equation.

On some nonlinear fractional PDEs in physics

“…The basic motivation of this paper is the extension of a very reliable and efficient technique namely Variational Iteration Method using Complex Transform (VIMCT) to find approximate solutions of time-fractional Fornberg-Whitham and system of time-fractional Wu-Zhang equations. The convergence of the proposed variational iteration method using fractional derivative is addressed in [28][29]. It is observed that the proposed algorithms is fully synchronized with the complexity of fractional differential equations, Numerical results coupled with graphical representations explicitly reveal the complete reliability and efficiency of the proposed algorithm.…”