Optimality conditions for the calculus of variations with higher-order delta derivatives

TL;DR

This paper establishes the Euler-Lagrange equations for calculus of variations problems involving higher-order delta derivatives on arbitrary time scales, extending classical results to a more general setting.

Contribution

It introduces optimality conditions for variational problems with higher-order delta derivatives on arbitrary time scales, broadening the scope of calculus of variations.

Findings

Derived Euler-Lagrange delta-differential equations for higher-order derivatives

Extended calculus of variations to arbitrary time scales

Provided a unified framework for delta calculus on time scales

Abstract

We prove the Euler-Lagrange delta-differential equations for problems of the calculus of variations on arbitrary time scales with delta-integral functionals depending on higher-order delta derivatives.