Generalized Transversality Conditions in Fractional Calculus of Variations

Abstract

Problems of calculus of variations with variable endpoints cannot be solved without transversality conditions. Here, we establish such type of conditions for fractional variational problems with the Caputo derivative. We consider: the Bolza-type fractional variational problem, the fractional variational problem with a Lagrangian that may also depend on the unspecified end-point $\varphi(b)$, where $x=\varphi(t)$ is a given curve, and the infinite horizon fractional variational problem.