*3.1. Problem Statement*

We first take fractional oscillators in Class I as a case to state the problems this research concerns with.

The analytical expressions with respect to the responses of free, impulse, step, to the oscillators of Class I are mathematically obtained (Mainardi [25], Achar et al. [33], Uchaikin ([38], Chapter 7)), also see Section 2.2 in this article. All noticed that a fractional oscillator of Class I is damping free in form but it is damped in nature due to fractional if 1 < *α* < 2. However, there are problems unsolved in this regard.

### **Problem 1.** *How to analytically represent the damping of Class I oscillators?*

In this article, we call the damping of fractional oscillators in Class I equivalent damping denoted by *ceq*1.

It is known that damping relates to mass. Therefore, if we find *ceq*1 in a fractional oscillator in Class I, its intrinsic mass must be different from the primary one *m* unless *α* = 2. We call it equivalent mass and denote it by *meq*1.
