Hamiltonian formalism of fractional systems

TL;DR

This paper develops a Hamiltonian formalism for fractional systems in classical mechanics, deriving fractional equations of motion and analyzing fractional oscillators, thus extending traditional mechanics to fractional derivatives.

Contribution

It introduces a Hamiltonian approach to fractional classical mechanics, including derivation of fractional equations of motion and analysis of fractional oscillators, expanding the theoretical framework.

Findings

Derived fractional equations of motion using Hamiltonian formalism

Analyzed behavior of fractional oscillators under various conditions

Discussed extension to continuous systems and interpretation of mechanics

Abstract

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional equations of motion are derived using the Hamiltonian formalism. The approach is illustrated with a simple-fractional oscillator in a free state and under an external force. Besides the behavior of the coupled fractional oscillators is analyzed. The natural extension of this approach to continuous systems is stated. The interpretation of the mechanics is discussed.