Fractional Noether's theorem in the Riesz-Caputo sense

TL;DR

This paper extends Noether's theorem to fractional variational problems involving Riesz-Caputo derivatives, providing both Lagrangian and Hamiltonian formulations with illustrative examples in fractional calculus and optimal control.

Contribution

It introduces a fractional Noether's theorem in the Riesz-Caputo sense, unifying Lagrangian and Hamiltonian approaches for fractional variational problems.

Findings

Established a fractional Noether's theorem for Riesz-Caputo derivatives

Derived Lagrangian and Hamiltonian formulations in the fractional context

Provided illustrative examples in fractional calculus and optimal control

Abstract

We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.