Higher-Order Calculus of Variations on Time Scales

TL;DR

This paper extends the calculus of variations on time scales by deriving higher-order Euler-Lagrange equations involving delta derivatives, broadening the theoretical framework for dynamic optimization.

Contribution

It introduces a higher-order Euler-Lagrange formulation for calculus of variations on time scales, which was not previously established.

Findings

Derived higher-order Euler-Lagrange equations on time scales.

Extended variational calculus to include higher-order delta derivatives.

Provided theoretical foundation for dynamic optimization problems on time scales.

Abstract

We prove a version of the Euler-Lagrange equations for certain problems of the calculus of variations on time scales with higher-order delta derivatives.