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Jianqu Zhu,Weidong Jin,Feng Guo 한국물리학회 2017 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.70 No.8
The stochastic resonance (SR) behavior for a linear oscillator with two kinds of fractional derivatives and random frequency is investigated. Based on linear system theory, and applying with the definition of the Gamma function and fractional derivatives, we derive the expression for the output amplitude gain (OAG). A stochastic multiresonance is found on the OAG curve versus the first kind of fractional derivative exponent. The SR occurs on the OAG as a function of the second kind of fractional exponent, as a function of the viscous damping and the friction coefficients, and as a function of the system’s frequency. The bona fide SR also takes place on the OAG curve versus the driving frequency.