Numerical Methods for Fractional Variational Problems Depending on Indefinite Integrals

Abstract

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 Grأ¼nwald–Letnikov formula. The fractional variational errors are discussed. Some numerical examples are given to illustrate these results.