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用变分迭代法解分数阶微分方程组 被引量：5

Solving Systems of Fractional Differential Equations by Variational Iteration Method
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摘要 用变分迭代法求解一类分数阶微分方程组,并改进了校正函数.数值结果表明,运用变分迭代法求解分数阶微分方程组的近似解有效且准确. The authors described approximate solutions for systems of fractional differential equations by the variational iteration method,and modified the correction function.Numerical results reveal that variational iteration method is very effective and accurate for obtaining approximate solutions of systems of fractional differential equations.
作者 代群 王长佳 李辉来
机构地区 长春理工大学理学院 吉林大学数学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2014年第5期901-905,共5页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11326078)
关键词 分数阶导数 方程组 变分迭代法 校正函数 fractional derivative system of equation variational iteration method correction function
分类号 O175.1 [理学—基础数学]
  • 相关文献

参考文献8

  • 1WU Yongyan, WANG Chun, LIAO Shijun. Solving the One Loop Soliton Solution of the Vakhnenko Equation by Means of the Homotopy Analysis Method [J]. Chaos, Solitons ~ Fractals, 2004, 23(5) : 1733-1740.
  • 2SONG I.ina, ZHANG Hongqing. Application of Homotopy Analysis Method to Fractional KdV-Burgers- Kuramoto Equation[J].Phys Lett A, 2007, 367(1/2): 88-94.
  • 3Lesnic D. The Decomposition Method for Initial Value Problems [J]. Appl Math Comput, 2006, 181(1): 206-213.
  • 4Jafari H, Daftardar-Gejji V. Solving a System of Nonlinear Fractional Differential Equations Using Adomain Decomposition [J]. J Comput Appl Math, 2006, 196(2): 644-651.
  • 5Odibat Z, Momani S. Modified Homotopy Perturbation Method: Application to Quadratic Riccati Differential Equation of Fractional Order[J]. Chaos, Solitons & Fractals, 2008, 36(1) : 167-174.
  • 6Momani S, Odibat Z. Numerical Comparison of Methods for Solving Linear Differential Equations of Fractional Order [J]. Chaos, Solitons & Fractals, 2007, 31(5) : 1248-1255.
  • 7代群,李辉来.一类非线性分数阶微分方程组的爆破解[J].吉林大学学报（理学版）,2012,50(1):1-5. 被引量：2
  • 8Odibat Z M, Shawagfeh N T. Generalized Taylor's Formula [J]. Appli Math Comput, 2007, 186(1): 286-293.

二级参考文献13

  • 1HE Ji-huan. Some Applications of Nonlinear Fractional Differential Equations and Their Approximations [ J ]. Bull Sci Technol, 1999, 15(2): 86-90.
  • 2HE Ji-huan. Approximate Analytical Solution for Seepage Flow with Fractional Derivative in Porous Media [ J]. Comput Methods Appl Mech Eng, 1998, 167(1/2) : 57-68.
  • 3Carpinteri A, Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics [ M ]. Berlin: Springer Verlag, 1997.
  • 4Shimizu N, ZHANG Wei. Fractional Calculus Approach to Dynamic Problems of Viscoelastic Materials [ J ]. JSME International Journal: Series C, Mechanical Systems, Machine Elements and Manufacturing, 1999, 42(4) : 825-837.
  • 5Jumarie G. Further Results on the Modelling of Complex Fractals in Finance, Scaling Observation and Optimal Portfolio Selection [ J ]. Systems Analysis, Modelling Simulation, 2002, 42 (10) : 1483-1499.
  • 6HU Yao-zhong, Oksendal B. Fractional White Noise Calculus and Applications to Finance [ J ]. Infinite Dim Anal Quantum Probab Related Topics, 2003, 6( 1 ) : 1-32.
  • 7Jumarie G. New Stochasti Fractional Models for Malthusian Growth, the Poissonian Birth Process and Optimal Management of Populations [ J ]. Math Comput Modelling, 2006, 44 (3/4) : 231-254.
  • 8Gorenflo R, Mainardi F. Fractional Calculus : Integral and Differential Equations of Fractional Order [ C ]//Fractals and Fractional Calculus in Continuum Mechanics Vienna: Springer-Verlag, 1997: 223-276.
  • 9Podlubny I. Fractional Differential Equation[ M]. New York: Academic Press, 1999.
  • 10Podlubny I. Geometric and Physical Interpretation of Fractional Integratiation and Fractional Differential [ J ]. Fract Calculus Appl Anal, 2002, 5: 367-386.

共引文献1

同被引文献35

  • 1谢涛.关键部件跌落冲击响应研究[J].包装工程,2005,26(2):77-78. 被引量：10
  • 2王志伟.粘滞阻尼三次函数弹性缓冲包装系统的跌落冲击响应[J].包装工程,1996,17(3):4-7. 被引量：24
  • 3王学彬,刘发旺.分离变量法解三维的分数阶扩散-波动方程的初边值问题[J].福州大学学报（自然科学版）,2007,35(4):520-525. 被引量：7
  • 4林永华,庄平辉,刘发旺.用分数阶高阶近似法解非线性分数阶常微分方程组[J].厦门大学学报（自然科学版）,2007,46(6):765-769. 被引量：1
  • 5HE Ji-huan. Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media[J]. Comput- er Methods in Applied Mechanics and Engineering, 1998,167 (1-2) : 57-68.
  • 6ZHANG Juan. The Numerical Solution of Fifth-order Bound- ary Value Problems by the Variational Iteration Method[J]. Computer and Mathematics with Applications, 2009, 58: 2347-2350.
  • 7HE Ji-huan. Exact Resonances of Nonlinear Vibration of Ro- tor-bearings System without Small Parameter[J]. Mechanics Research Communications, 2000,27 (4) : 451-456.
  • 8HE Ji-huan, WUA Xu-Hong. Variational Iteration Method: New Development and Applications[J]. Computers and Mathe- matics with Applications, 2007,54 (7-8) : 881-894.
  • 9HE Ji-huan. Variational Iteration Method-Some Recent Re- suits and New Interpretation[J]. Journal of Computational and Applied Mathematics ,2007,207 ( 1 ) :3-17.
  • 10HE Ji-huan. The Variational Approach Coupled with an Ancient Chinese Mathematical Method to the Relativistic Oscil- lator[J]. Mathematical and Computational Applications, 2010, 15(5) :930-935.

引证文献5

二级引证文献8

吉林大学学报（理学版）
2014年 第5期

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