Resonant behavior of a fractional oscillator with fluctuating mass

We examine the phenomenon of stochastic resonance of a fractional oscillator that has a random mass and is subject to an external periodic force. The colored fluctuations of the oscillator mass are modeled as a dichotomous noise. The viscoelastic type friction kernel with memory is assumed as a power law function in time. An exact formula for the complex susceptibility of the oscillator is derived, and the dependence of the spectral amplification on system parameters is investigated. It is established that in certain regions of the system parameters an interplay of multiplicative noise and memory can generate a bona fide multiresonance versus the driving frequency as well as stochastic resonance vs noise parameters. Influence of the memory exponent in the resonance regimes of the oscillator is also investigated. Particularly, it is shown that the results about stochastic resonance in the model considered are significantly different from recently obtained results for fractional oscillators with fluctuating frequency and with fluctuating damping.