Abstract
Into this paper, the amplitude-frequency and phase-frequency characteristics of the Van der Polar fractional oscillator are studied in order to establish their relationship with the orders of fractional derivatives included in the model equation. Using the harmonic balance method, analytical formulas were obtained for the amplitude-frequency, phase-frequency characteristics, as well as the quality factor – the energy characteristic of the oscillatory system. It was shown that the quality factor depends on the orders of fractional derivatives, and change in their values can lead to both an increase and a decrease in the quality factor.
Highlights
At present, fractional oscillators, mathematical models of oscillatory systems with memory effects, are of great interest to researchers [1, 2]
It was shown in [7, 8] that the orders of fractional derivatives are related to the quality factor of the oscillatory system and this is of very important practical importance
We investigated the forced oscillations of a fractional oscillator of Van der Pol – an analog of the Van der Pol oscillator
Summary
Fractional oscillators, mathematical models of oscillatory systems with memory effects, are of great interest to researchers [1, 2]. Fractional oscillators are described using fractional derivatives, which are studied in the framework of the theory of fractional integro-differentiation [6] It was shown in [7, 8] that the orders of fractional derivatives are related to the quality factor of the oscillatory system and this is of very important practical importance. Analytical formulas are obtained for the amplitude-frequency (AFC) and phase-frequency (PFC) characteristics, as well as the quality factor of the oscillatory system
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