Fractional derivative order determination from harmonic oscillator damping factor
Classical Physics
2020-07-14 v1
Abstract
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless. Afterwards, approximated expressions that relate the two equations parameters for the case that the fractional order is close to an integer number are presented. Following, a numerical regression is made using power series expansion, and, also from fractional calculus, the fact that both equations cannot be equivalent is concluded. In the end, from the numerical regression data, the analytical approximated expressions that relate the two equations' parameters are refined.
Cite
@article{arxiv.2002.02479,
title = {Fractional derivative order determination from harmonic oscillator damping factor},
author = {Luís Felipe Alves da Silva and Valdiney Rodrigues Pedrozo Júnior and João Vítor Batista Ferreira},
journal= {arXiv preprint arXiv:2002.02479},
year = {2020}
}
Comments
10 pages, 5 figures