The second Noether theorem on time scale

TL;DR

This paper extends the second Noether theorem to variational problems on time scales, unifying classical, $h$-calculus, and $q$-calculus cases within a single framework.

Contribution

It introduces a generalized second Noether theorem applicable to variational problems on arbitrary time scales, encompassing several specific calculus cases.

Findings

Unified second Noether theorem on time scales

Derivation of classical, $h$-calculus, and $q$-calculus results as corollaries

Provides a broad theoretical framework for variational calculus

Abstract

We extend the second Noether theorem to variational problems on time scales. Our result provides as corollaries the classical second Noether theorem, the second Noether theorem for the $h$-calculus and the second Noether theorem for the $q$-calculus.