Anomalous diffusion of a fractional harmonic oscillator driven by both thermal noise and additive impulsive noise is investigated. By using the Laplace and double Laplace transform techniques, the mean, variance, correlation function and mean square displacement (MSD) of the oscillator are expressed by generalized Mittag-Leffler functions with three parameters. Furthermore, asymptotic diffusive behavior of the oscillator is investigated in terms of the asymptotic properties of generalized Mittag-Leffler function. It is shown that the impulsive noise enhances the ballistic diffusion of the oscillator for short time-lag and adds a constant to the mean square displacement for long time-lag.
