Stochastic resonance in a harmonic oscillator with fractional-order external and intrinsic dampings

In this paper, the phenomenon of stochastic resonance (SR) in a harmonic oscillator with fractional-order external and intrinsic dampings under the external periodic force is investigated. Applying the Shapiro–Loginov formula, fractional Shapiro–Loginov formula, generalized fractional Shapiro–Loginov formula and the Laplace transform technique, we obtain the analytic expressions of the first moment and the amplitude of the output signal. By studying the impacts of the driving frequency, system parameters and the noise parameters, we find the non-monotonic behaviors of the output amplitude. The results indicate that the bona fide SR, the generalized SR and the conventional SR phenomena occur in the proposed model. Furthermore, the numerical simulations are presented to verify the effectiveness of the analytic result.