Generalized Transversality Conditions in Fractional Calculus of Variations

TL;DR

This paper derives transversality conditions for fractional calculus of variations problems involving Caputo derivatives, addressing variable endpoints, endpoint dependencies, and infinite horizon cases.

Contribution

It establishes new transversality conditions for fractional variational problems with Caputo derivatives, including Bolza-type, endpoint-dependent, and infinite horizon scenarios.

Findings

Derived transversality conditions for fractional variational problems

Extended conditions to problems with endpoint dependencies

Addressed infinite horizon fractional variational problems

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.