  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.
