Lagrangians with linear velocities within Riemann-Liouville fractional derivatives

TL;DR

This paper explores Lagrangians linear in velocities using fractional calculus, deriving Euler-Lagrange equations, solving specific examples explicitly, and discussing how classical results are recovered within this fractional framework.

Contribution

It introduces a fractional calculus approach to analyze Lagrangians linear in velocities and derives corresponding Euler-Lagrange equations, providing explicit solutions and connecting to classical mechanics.

Findings

Explicit solutions for fractional Euler-Lagrange equations

Recovery of classical results within fractional calculus

Application of fractional derivatives to Lagrangian mechanics

Abstract

Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the recovery of the classical results was discussed.