Fractional Hamilton formalism within Caputo's derivative

TL;DR

This paper develops a fractional Hamiltonian formalism using Caputo derivatives, providing new expressions for canonical momenta and Hamiltonian, and demonstrating their equivalence with fractional Euler-Lagrange equations.

Contribution

It introduces a fractional Hamiltonian framework with explicit formulas for canonical momenta and Hamiltonian based on Caputo derivatives, linking it to existing fractional Euler-Lagrange equations.

Findings

Derived fractional Hamiltonian and canonical momenta expressions

Established equivalence with fractional Euler-Lagrange equations

Validated framework with an example

Abstract

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.