Constants of motion for fractional action-like variational problems

TL;DR

This paper extends Noether's symmetry theorem to fractional calculus of variations, specifically for Riemann-Liouville integral functionals, providing new insights into constants of motion in fractional variational problems.

Contribution

It introduces a fractional version of Noether's theorem for Riemann-Liouville integral functionals in the calculus of variations.

Findings

Derived new constants of motion for fractional variational problems

Extended classical symmetry principles to fractional calculus

Provided theoretical framework for fractional Noether's theorem

Abstract

We extend Noether's symmetry theorem to the fractional Riemann-Liouville integral functionals of the calculus of variations recently introduced by El-Nabulsi.