Fractional derivative order determination from harmonic oscillator damping factor

Luís Felipe Alves da Silva; Valdiney Rodrigues Pedrozo Júnior; João Vítor Batista Ferreira

doi:10.1016/j.cjph.2020.04.020

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arXiv · 2002.02479

Fractional derivative order determination from harmonic oscillator damping factor

Luís Felipe Alves da Silva·Valdiney Rodrigues Pedrozo Júnior·João Vítor Batista Ferreira

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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.

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Luís Felipe Alves da Silva, Valdiney Rodrigues Pedrozo Júnior, João Vítor Batista Ferreira. 2020-02-06. Fractional derivative order determination from harmonic oscillator damping factor. https://doi.org/10.1016/j.cjph.2020.04.020

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