The Variational Iteration Method Of Fractional Differential Equations

The variational iteration method (VIM) has been proved to be a powerful math-ematical tool for solving various types of linear and nonlinear problems.In this paper,the basic idea of the variational iteration method(VIM)is intro-duced,and it's convergence is proofed.The method is successfully applied to solving some kinds of fractional differential equations.The results reveal that the method is very effective and convenient for solving fractional differential equations.This paper is composed of four chapters.In chapter l,we briefly introduce the research status of this paper and the main work of the paper.In chapter 2,some basic theory of the fractional calculus and the theory of varia-tional are introduced.We expound the basic definitions of fractional calculus theory: Riemann-Liouville fractional integrals;Riemann-Liouville fractional derivatives; Caputo fractional derivatives;discuss basic operation nature.The definitions and the basic lemmas of variation are introduced.In chapter 3,we mainly introduce the basic ideas of the variational iteration method and the convergence of the variational iteration method is studied.Some exam-ples are used to test the convergence of the method. The basic ideas of the variational iterative method is showed, the general solving iterative formulas are constructed.In chapter 4,we briefly investigate some application of the variational iteration method in fractional differential equations. The modified variational iteration method is used to solving factional integro-differential equations.