Noether's symmetry theorem for nabla problems of the calculus of variations

TL;DR

This paper extends Noether's symmetry theorem and DuBois-Reymond conditions to nabla calculus of variations on time scales, unifying continuous and discrete cases.

Contribution

It introduces a Noether-type symmetry theorem and a DuBois-Reymond condition specifically for nabla calculus of variations on time scales, broadening the theoretical framework.

Findings

Established a Noether-type symmetry theorem for nabla problems

Derived a DuBois-Reymond necessary condition for optimality

Unified continuous and discrete calculus of variations on time scales

Abstract

We prove a Noether-type symmetry theorem and a DuBois-Reymond necessary optimality condition for nabla problems of the calculus of variations on time scales.