Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

TL;DR

This paper develops a Lagrangian framework for classical fields incorporating Riemann-Liouville fractional derivatives, deriving fractional Euler-Lagrange equations and illustrating their application through two examples.

Contribution

It introduces a fractional Lagrangian formulation for classical fields using Riemann-Liouville derivatives, extending traditional field theory methods.

Findings

Derived fractional Euler-Lagrange equations for classical fields.

Presented two example applications of the fractional formulation.

Abstract

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.