Convergence of the variational iteration method for solving multi-order fractional differential equations

Authors:
Shuiping Yang;Aiguo Xiao;Hong Su
Affiliations:
School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan, 411105, China and Department of Mathema ...;School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan, 411105, China;School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Hunan, 411105, China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this paper, the variational iteration method (VIM) is applied to obtain approximate solutions of multi-order fractional differential equations (M-FDEs). We can easily obtain the satisfying solution just by using a few simple transformations and applying the VIM. A theorem for convergence and error estimates of the VIM for solving M-FDEs is given. Moreover, numerical results show that our theoretical analysis are accurate and the VIM is a powerful method for solving M-FDEs.