Fractional Classical Mechanics

TL;DR

This paper introduces fractional classical mechanics as a classical analogue to fractional quantum mechanics, developing its theoretical framework, equations of motion, and analyzing a fractional oscillator model with novel period equations.

Contribution

It presents the formulation of fractional classical mechanics, including Lagrangian, Hamiltonian, and Hamilton-Jacobi frameworks, and introduces a fractional oscillator model with new period equations.

Findings

Derived equations of motion for fractional classical mechanics

Solved the fractional oscillator model in 1D

Discussed the relationship between fractional classical and quantum oscillators

Abstract

Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics. The Lagrangian of fractional classical mechanics has been introduced, and equation of motion has been obtained. Fractional oscillator model has been launched and solved in 1D case. A new equation for the period of oscillations of fractional classical oscillator has been found. The interplay between the energy dependency of the period of classical oscillations and the non-equidistant distribution of the energy levels for fractional quantum oscillator has been discussed. We discuss as well, the relationships between new equations of fractional classical mechanics and the well-known fundamental equations of classical mechanics.