Quality factor of forced oscillations of a linear fractional oscillator

Analytical formulas for the amplitude–frequency and phase–frequency characteristics, as well as forced oscillations, of a fractional oscillator have been derived using the harmonic balance method. It has been found that these characteristics depend on the dissipative properties of a medium–memory effects, which are described by fractional-order derivatives. It has been shown that fractional orders of derivatives influence the decay of the oscillatory process and are related to its Q factor. Analytical curves of forced oscillation characteristics for a linear fractional oscillator give the idea that fractional orders can be considered as control parameters for an oscillatory process in a dissipative medium.