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

被引：66
|
作者：
Yang, Shuiping [1 ,2 ]
Xiao, Aiguo [1 ]
Su, Hong [1 ]
机构：
[1] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
[2] Huizhou Univ, Dept Math, Huizhou 516007, Guangdong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 60卷 / 10期
关键词：
Fractional differential equations; Variational iteration method; Convergence; Fractional calculus; NUMERICAL-SOLUTION; INTEGRAL-EQUATIONS; SIMULATION; SYSTEMS; VOLTERRA;
D O I：
10.1016/j.camwa.2010.09.044
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：2871 / 2879
页数：9
相关论文
共 50 条
  • [21] Variational Iteration Method for Solving Fractional Integro-Differential Equations with Conformable Differointegration
    Damak, Mondher
    Mohammed, Zaid Amer
    AXIOMS, 2022, 11 (11)
  • [22] Variational iteration transform method for fractional differential equations
    Ziane, Djelloul
    Cherif, Mountassir Hamdi
    JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2018, 21 (01) : 185 - 199
  • [23] Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
    Yin, Fukang
    Song, Junqiang
    Leng, Hongze
    Lu, Fengshun
    SCIENTIFIC WORLD JOURNAL, 2014,
  • [24] Analysis of Multi Term Fractional Differential Equations using Variational Iteration Method
    Shaikh, Amjad S.
    Jadhav, Vikas S.
    Sontakke, Bhausaheb R.
    Nisar, Kottakkaran S.
    PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2022, 54 (01): : 15 - 31
  • [25] An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations
    Y. Talaei
    M. Asgari
    Neural Computing and Applications, 2018, 30 : 1369 - 1376
  • [26] An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations
    Talaei, Y.
    Asgari, M.
    NEURAL COMPUTING & APPLICATIONS, 2018, 30 (05): : 1369 - 1376
  • [27] Multi-order fractional differential equations and their numerical solution
    Diethelm, K
    Ford, NJ
    APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (03) : 621 - 640
  • [28] LOCAL FRACTIONAL VARIATIONAL ITERATION TRANSFORM METHOD: A TOOL FOR SOLVING LOCAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
    Jafari, Hossein
    Jassim, Hassan kamil
    Ansari, Ali
    Nguyen, Van thinh
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2024, 32 (04)
  • [29] A stable minimal search method for solving multi-order fractional differential equations based on reproducing kernel space
    Wu, Longbin
    Chen, Zhong
    Ding, Xiaohua
    NUMERICAL ALGORITHMS, 2021, 87 (04) : 1707 - 1727
  • [30] A stable minimal search method for solving multi-order fractional differential equations based on reproducing kernel space
    Longbin Wu
    Zhong Chen
    Xiaohua Ding
    Numerical Algorithms, 2021, 87 : 1707 - 1727
12345