Backward variational approach on time scales with an action depending on the free endpoints

TL;DR

This paper develops necessary optimality conditions for variational problems on time scales with actions depending on free endpoints, using the backward nabla calculus, and introduces new transversality conditions.

Contribution

It extends the calculus of variations on time scales by incorporating endpoint-dependent actions and deriving new transversality conditions with the backward nabla approach.

Findings

Established necessary optimality conditions for endpoint-dependent variational problems.

Derived new transversality conditions on time scales.

Utilized the backward nabla differential operator for generality.

Abstract

We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator.