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Research Papers

Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals

[+] Author and Article Information
Dongling Wang

e-mail: wdyxtu@hotmail.com

Aiguo Xiao

e-mail: xag@xtu.edu.cn
Hunan Key Laboratory for Computation and Simulation in Science and Engineering,
Key Laboratory of Intelligent Computing &
Information Processing of Ministry of Education,
Xiangtan University,
Xiangtan, Hunan 411105, PRC

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received August 24, 2012; final manuscript received October 8, 2012; published online November 15, 2012. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 8(2), 021018 (Nov 15, 2012) (7 pages) Paper No: CND-12-1132; doi: 10.1115/1.4007858 History: Received August 24, 2012; Revised October 08, 2012

In this paper, the fractional variational integrators for fractional variational problems depending on indefinite integrals in terms of the Caputo derivative are developed. The corresponding fractional discrete Euler–Lagrange equations are derived. Some fractional variational integrators are presented based on the Grünwald–Letnikov formula. The fractional variational errors are discussed. Some numerical examples are given to illustrate these results.

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Figures

Grahic Jump Location
Fig. 1

Numerical solutions on lines with markers and true solutions on solid lines for different values of α with N = 80 (♦:α = 0.1,°:α = 0.4,▹:α = 0.7,⋆:α = 0.9)

Grahic Jump Location
Fig. 2

Numerical solutions on lines with markers and true solutions on solid lines for different values of α with N = 80 (♦:α = 0.2,•:α = 0.5,*:α = 0.8,°:α = 0.95)

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