Noisy fractional oscillator: Temporal behavior of the autocorrelation function

Abstract: The influence of external and internal noises on the output signal of a fractional Langevin equation with the friction kernel of a viscoelastic type is considered. The interaction with fluctuations of environmental parameters is modeled by a multiplicative white noise and by an additive noise with a zero mean. In the case of an external harmonic driving force it is shown that additive external and internal noises cause qualitatively different behaviors of the autocorrelation function for the output signal. Particularly, in the case of external noise it is established that at a sufficiently strong memory of the friction kernel the output signal corresponds to trapped dynamics in an effective potential well even if the system is subdiffusive in the case of internal noise.