Damping characteristics of a fractional oscillator

A study of sinusoidally forced oscillations of a fractional oscillator shows that the system exhibits a rich variety of damping characteristics. While some aspects of the damping mimic the characteristic features of a damped harmonic oscillator, there are others, which do not find any parallel in the damped harmonic oscillator system. It is clearly demonstrated that the “free” and “forced” oscillations of a fractional oscillator are characterized by different damping parameters. While both depend on the fractional index α, the “free” oscillation damping depends on the “natural frequency”, ω0, of the oscillator, the “forced” oscillation damping depends in addition, on the “driving frequency”, ω. Furthermore, there is a different power-law tail associated with each of these cases.