  The problem of biological motion is a very intriguing and topical issue. Many
efforts are being focused on the development of novel modeling approaches for
the description of anomalous diffusion in biological systems, such as the very
complex and heterogeneous cell environment. Nevertheless, many questions are
still open, such as the joint manifestation of statistical features in
agreement with different models that can be also somewhat alternative to each
other, e.g., Continuous Time Random Walk (CTRW) and Fractional Brownian Motion
(FBM). To overcome these limitations, we propose a stochastic diffusion model
with additive noise and linear friction force (linear Langevin equation), thus
involving the explicit modeling of velocity dynamics. The complexity of the
medium is parameterized via a population of intensity parameters (relaxation
time and diffusivity of velocity), thus introducing an additional randomness,
in addition to white noise, in the particle's dynamics. We prove that, for
proper distributions of these parameters, we can get both Gaussian anomalous
diffusion, fractional diffusion and its generalizations.
