Amplitude-Frequency and Phase-Frequency Performances of Forced Oscillations of a Nonlinear Fractional Oscillator

Abstract

The relationship is substantiated between the amplitude-frequency and phase-frequency performances of forced oscillations of a nonlinear fractional oscillator and the orders of fractional derivatives in its model equation. Using computer simulation, it is shown that the orders of fractional derivatives are related with the quality factor of an oscillatory system. A decrease in the superior order (“fractional” inertia) leads to a decrease in the quality factor, while a decrease in the inferior order (“fractional” friction) leads to an increase in the quality factor. We have compared numerical calculations of the amplitude-frequency and phase-frequency performances for a linear fractional oscillator with the calculation results obtained using analytical formulas of other authors. The analysis has shown a good agreement between these calculations, confirming the correctness of the numerical calculations presented.