The problem of biological motion is a very intriguing and topical issue.
Many efforts are being focused on the development of novel modelling
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 also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian
motion. To overcome these limitations, we propose a stochastic diffusion
model with additive noise and linear friction force (linear Langevin equation),
thus involving the explicit modelling of velocity dynamics. The complexity of
the medium is parametrized 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.V.S. acknowledges BCAM Internship Program, Bilbao, for the financial support to her internship research period during which she developed her master’s thesis research
useful for her master’s degree in Physics at University of Bologna.
S.V. acknowledges the University of Bologna for the financial support
through the ‘Marco Polo Programme’ for her PhD research period
abroad spent at BCAM, Bilbao, useful for her PhD degree in Physics
at University of Bologna.
P.P. acknowledges financial support from Bizkaia Talent and European Commission
through COFUND scheme, 2015 Financial Aid Program for Researchers, project number
AYD–000–252 hosted at BCAM, Bilbao