Generalized Euler-Lagrange equations for variational problems with scale derivatives

TL;DR

This paper derives generalized Euler-Lagrange equations for variational problems involving scale derivatives, accommodating multiple derivatives, parameters, and higher-order derivatives on Hölder curves.

Contribution

It introduces new Euler-Lagrange equations for complex variational functionals with scale derivatives, expanding the theoretical framework.

Findings

Derived Euler-Lagrange equations for multiple scale derivatives

Extended equations to include parameter-dependent Lagrangians

Addressed higher-order scale derivatives in variational calculus

Abstract

We obtain several Euler-Lagrange equations for variational functionals defined on a set of H\"older curves. The cases when the Lagrangian contains multiple scale derivatives, depends on a parameter, or contains higher-order scale derivatives are considered.