Transient superdiffusion in random walks with a qq-exponentially decaying memory profile

•The Fokker–Planck equation is derived with an implicit qq-dependence associated with the memory size.•These results broaden our knowledge on the importance of the diffusive properties of the walker.•The results shown here pave the way for treating other non-Markovian memory patterns in future work.

We propose a random walk model with qq-exponentially decaying memory profile. The qq-exponential function is a generalization of the ordinary exponential function. In the limit q→1q→1, the qq-exponential becomes the ordinary exponential function. This model presents a Markovian diffusive regime that is characterized by finite memory correlations. It is well known, that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. In this problem we report the outcome of a transient superdiffusion for finite sized walks.