Remarks on the calculus of variations on time scales

TL;DR

This paper discusses the current state of the calculus of variations on time scales, highlighting that existing formulations are still heuristic rather than fully rigorous.

Contribution

It emphasizes the need for more rigorous formulations in the calculus of variations on time scales, contrasting with the classical, well-established theory.

Findings

Current formulations are heuristic

Lack of rigorous results on time scales

Calls for formalization of the theory

Abstract

The calculus of variations is a classical subject which has gain throughout the last three hundred years a level of rigor and elegance that only time can give. In this note we show that, contrary to the classical field, available formulations and results on the recent calculus of variations on time scales are still at the heuristic level.