The stochastic resonance (SR) phenomenon for a nonlinear system with fractional derivative driven by multiplicative and additive noise is investigated. Applying the generalized harmonic function approach and the adiabatic elimination theory, the signal-to-noise ratio (SNR) for the system is obtained. It is found that the SNR manifests SR behavior with the variety of the system parameters, with the variety of the system characteristic frequency and that of the strength of external additive noise. The SNR behaves nonmonotonically with the system fractional exponent.

中文翻译：

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分数阶导数受乘加性噪声影响的非线性系统的共振现象

研究了由乘法和加性噪声驱动的具有分数导数的非线性系统的随机共振（SR）现象。应用广义谐波函数法和绝热消除理论，得到了系统的信噪比（SNR）。发现SNR随系统参数的变化，系统特征频率的变化以及外部加性噪声强度的变化而表现出SR特性。SNR与系统分数指数表现为非单调。