  A model for anomalous transport of tracer particles diffusing in complex
media in two dimensions is proposed. The model takes into account the
characteristics of persistent motion that active bath transfer to the tracer,
thus the model proposed in here extends active Brownian motion, for which the
stochastic dynamics of the orientation of the propelling force is described by
scale Brownian motion (sBm), identified by a the time dependent diffusivity of
the form $D_\beta\propto t^{\beta-1}$, $\beta>0$. If $\beta\neq1$, sBm is
highly non-stationary and suitable to describe such a non-equilibrium dynamics
induced by complex media. In this paper we provide analytical calculations and
computer simulations to show that genuine anomalous diffusion emerge in the
long-time regime, with a time scaling of the mean square displacement
$t^{2-\beta}$, while ballistic transport $t^2$, characteristic of persistent
motion, is found in the short-time one. An analysis of the time dependence of
the kurtosis, and intermediate scattering function of the positions
distribution, as well as the propulsion auto-correlation function, which
defines the effective persistence time, are provided.
