Towards a combined fractional mechanics and quantization

TL;DR

This paper introduces a fractional Hamiltonian formalism that extends classical mechanics to systems with combined Caputo fractional derivatives, enabling quantization of nonconservative systems.

Contribution

It develops a fractional Hamiltonian framework and generalizes the Hamilton-Jacobi equation for combined fractional derivatives, facilitating quantization of nonconservative systems.

Findings

Formulated a fractional Hamiltonian formalism for combined Caputo derivatives.

Generalized Hamilton-Jacobi equation for fractional systems.

Provided tools for quantizing nonconservative fractional systems.

Abstract

A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional derivatives. The obtained results provide tools to carry out the quantization of nonconservative problems through combined fractional canonical equations of Hamilton type.