Lagrangian and Hamiltonian Formulations of the Damped Harmonic Oscillator Using Caputo Fractional Derivative

Abstract

In this work, the Caputo fractional derivative is used to construct the Lagrangian and the Hamiltonian formulations for nonconservative mechanical systems. The Euler-Lagrange equations are derived using a variational principle. Hamilton’s equations of motion are then obtained by introducing a set of momenta and a Hamiltonian in a manner that is more consistent with that used in conventional classical mechanics. The proposed formalism is applied to the damped harmonic oscillator, as an example.