Variational problems for Holderian functions with free terminal point

TL;DR

This paper extends variational calculus to nondifferentiable functions using the scale derivative, addressing problems with free terminal points and exploring various constraints and orders.

Contribution

It introduces a new framework for nondifferentiable variational problems using the scale derivative, generalizing classical calculus of variations.

Findings

Developed variational problems with free terminal points using scale derivatives

Analyzed constrained and unconstrained nondifferentiable variational problems

Extended to higher-order variational problems for nondifferentiable functions

Abstract

We develop the new variational calculus introduced in 2011 by J. Cresson and I. Greff, where the classical derivative is substituted by a new complex operator called the scale derivative. In this paper we consider several nondifferentiable variational problems with free terminal point: with and without constraints, of first and higher-order type.