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Numerical Solution for Fractional-Order Differential Systems with Time-Domain and Frequency-Domain Methods 被引量：1

Numerical Solution for Fractional-Order Differential Systems with Time-Domain and Frequency-Domain Methods
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摘要 For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed. For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.
作者 Ke Xiao Shang-Bo Zhou Wei-Wei Zhang
机构地区 Computer Department of Chongqing University
出处 《Journal of Electronic Science and Technology of China》 2008年第3期294-298,共5页 中国电子科技（英文版）
基金 the Natural Science Foundation of CQ CSTC under Grant No. 2007BB2161.
关键词 Analytical solution frequency domain fractional order numerical solution time domain Analytical solution frequency domain fractional order numerical solution time domain
分类号 O343.1 [理学—固体力学]
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参考文献10

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  • 1蔡新,刘发旺.解空间Riesz分数阶扩散方程的一种数值方法[J].高等学校计算数学学报,2005,27(S1):242-246. 被引量：4
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  • 3Fetecaua C,Atharb M, Fetecau C. Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate [ J]. Computers and Mathematics with Applications, 2009,57:596 - 603.
  • 4Xu Hang, Liao Shi-Jun, You Xiang-Cheng. Analysis of nonlinear fractional partial differential equations with the homotopy analysis method[ J]. Commun Nonlinear Sci Numer Simulat, 2009,14 : 1152 - 1156.
  • 5Bouafoura M K, Braiek N B. PIλDμ controller design for integer and fractional plants using piecewise orthogonal functions[J]. Communications in Nonlinear Science and Numerical Simulation, 2010,15 (5) : 1267-1278.
  • 6Marom O, Momoniat E. A comparison of numerical solutions of fractional diffusion models in finance[Jl. Nonlinear Analysis: Real World Applications, 2009, 10 ( 6 ) : 3435 - 3442.
  • 7Wu J L. A wavelet operational method for solving fractional partial differential equations numerically[ J]. Applied Mathematics and Computation ,2009,214:31-40.
  • 8Yang Q, Liu F, Turner I. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives[J]. Appl. Math. Modell,2010,34(1 ):200-218.
  • 9Zhou Shangbo, Li Hua, Zhu Zhengzhou. Chaos control and synchronization in a fractional neural network system [ J ]. Chaos, Solitons and Fractals ,2008,36 (4) :973-984.
  • 10蒲亦非,王卫星.数字图像的分数阶微分掩模及其数值运算规则[J].自动化学报,2007,33(11):1128-1135. 被引量：70

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Journal of Electronic Science and Technology of China
2008年 第3期

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