  In recent years a huge interdisciplinary field has emerged which is devoted
to the complex dynamics of anomalous transport with long-time memory and
non-markovian features. It was found that the framework of fractional calculus
and its generalizations are able to capture these phenomena. Many of the
classical models are based on continuous-time renewal processes and use the
Montroll Weiss continuous time random walk (CTRW) approach. On the other hand
their discrete time counterparts are rarely considered in the literature
despite their importance in various applications. The goal of the present paper
is to give a brief sketch of our recently introduced discrete-time Prabhakar
generalization of the fractional Poisson process and the related discrete-time
random walk (DTRW) model. We show that this counting process is connected with
the continuous time Prabhakar renewal process by a (well scaled)
continuous-time limit. We deduce the state probabilities and discrete time
generalized fractional Kolmogorov-Feller equations governing the Prabhakar DTRW
and discuss effects such as long time memory (nonmarkovianity) as a hallmark of
the complexity of the process.
