Variational Procedure for Higher-Derivative Mechanical Models in a Fractional Integral Framework

TL;DR

This paper develops Lagrangian and Hamiltonian methods for higher-derivative mechanical models using fractional calculus, providing new insights into their physical and geometric interpretations.

Contribution

It introduces a fractional integral framework for higher-order equations of motion, expanding traditional mechanics with novel mathematical and interpretative tools.

Findings

Effective formulation of higher-order equations using fractional calculus

Discussion of physical and geometric interpretations

Application to a higher-order harmonic oscillator

Abstract

We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its efficacy and difficulties. We also present the physical and geometric interpretations for the approach we pursue and present the details of a higher-order harmonic oscillator.