A survey on fractional variational calculus

Abstract

Main results and techniques of the fractional calculus of variations are surveyed. We consider variational problems containing Caputo derivatives and study them using both indirect and direct methods. In particular, we provide necessary optimality conditions of Euler-Lagrange type for the fundamental, higher-order, and isoperimetric problems, and we compute approximate solutions based on truncated Grünwald-Letnikov approximations of the Caputo derivatives.