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.
Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals
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.
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Wang, D., and Xiao, A. (November 15, 2012). "Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals." ASME. J. Comput. Nonlinear Dynam. April 2013; 8(2): 021018. https://doi.org/10.1115/1.4007858
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