A formulation of the fractional Noether-type theorem for multidimensional Lagrangians

TL;DR

This paper extends the classical Noether theorem to fractional calculus, deriving Euler-Lagrange equations for multidimensional fractional variational problems and proving a fractional Noether-type theorem for various physical systems.

Contribution

It introduces a fractional Noether-type theorem for multidimensional Lagrangians using Riemann-Liouville derivatives, advancing the theoretical framework of fractional variational calculus.

Findings

Derived Euler-Lagrange equations for fractional variational problems with multiple integrals

Proved a fractional Noether-type theorem applicable to conservative and nonconservative systems

Utilized Riemann-Liouville fractional derivatives in the formulation

Abstract

This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the Riemann-Liouville fractional derivative.