Nondifferentiable variational principles in terms of a quantum operator

TL;DR

This paper extends variational calculus to nondifferentiable functions using quantum operators, addressing various problems with constraints, multiple variables, and different orders.

Contribution

It introduces a nondifferentiable calculus of variations framework based on quantum operators for H"older functions, covering diverse problem types.

Findings

Developed a new calculus for nondifferentiable variational problems.

Applied the framework to multiple quantum variational problems.

Demonstrated the approach's versatility across different problem settings.

Abstract

We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first and higher-order type.