Fractional derivative order determination from harmonic oscillator damping factor.
SILVA, Luís Felipe Alves da; PEDROZO JÚNIOR, Valdiney Rodrigues; FERREIRA, João Vítor Batista.
SILVA, Luís Felipe Alves da; PEDROZO JÚNIOR, Valdiney Rodrigues; FERREIRA, João Vítor Batista.
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. Approximated expressions that relate the two equations parameters, when fractional order is close to an integer, 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.
@article={003000758,author = {SILVA, Luís Felipe Alves da; PEDROZO JÚNIOR, Valdiney Rodrigues; FERREIRA, João Vítor Batista.},title={Fractional derivative order determination from harmonic oscillator damping factor},journal={Chinese Journal of Physics},note={v. 66, p. 673-683},year={2020}}