  We present a modelling approach for diffusion in a complex medium
characterized by a random length scale. The resulting stochastic process shows
subdiffusion with a behavior in qualitative agreement with single particle
tracking experiments in living cells, such as ergodicity breaking, p-variation
and aging. In particular, this approach recapitulates characteristic features
previously described in part by the fractional Brownian motion and in part by
the continuous-time random walk. Moreover, for a proper distribution of the
length scale, a single parameter controls the ergodic-to-nonergodic transition
and, remarkably, also drives the transition of the diffusion equation of the
process from non-fractional to fractional, thus demonstrating that fractional
kinetics emerges from ergodicity breaking.
