Amplitude-frequency and phase-frequency characteristics of forced vibrations of nonlinear fractional oscillator

In the work, using the amplitude-frequency (AFC) and phase-frequency characteristics (PFC) of forced oscillations of a non-linear fractional oscillator, their connection with the orders of fractional derivatives, which are included in its model equation, is substantiated. It is shown, using computer simulation, that the orders of fractional derivatives are related to the quality factor of an oscillatory system. A decrease in the higher order (“fractional” inertia) leads to a decrease in the quality factor, and a decrease in the lower order (“fractional” friction) leads to an increase in the quality factor. Therefore, we come to two mechanisms for controlling the Q of the oscillatory system, where the orders of fractional derivatives play the role of control parameters.