Fractional variational integrators for fractional variational problems

In this paper, the fractional variational integrators for a class of fractional variational problems are developed. The fractional discrete Euler–Lagrange equation is obtained. Based on the Grünwald–Letnikov method and Diethelm’s fractional backward differences, some fractional variational integrators are presented and the fractional variational errors are discussed. Some numerical examples are presented to illustrate these results.

► The fractional variational integrators for a class of fractional variational problems are developed.
► Fractional discrete Euler–Lagrange equation is obtained.
► Some fractional variational integrators are presented and the fractional variational errors are discussed.
► Some numerical examples are also given.