Abstract The Mittag–Leffler function is universally acclaimed as the Queen function of
fractional calculus. The aim of this work is to survey the key results and applications …

We survey the 'generalized fractional Poisson process'(GFPP). The GFPP is a renewal
process generalizing Laskin's fractional Poisson counting process and was first introduced …

We introduce a compartment model with memory for the dynamics of epidemic spreading in
a constant population of individuals. Each individual is in one of the states S= susceptible, I …

Closed-form multi-dimensional solutions and asymptotic behaviours for subdiffusive processes
with crossovers: II. Accelerating case - IOPscience Skip to content IOP Science home …

This paper addresses the generalization of counting processes through the age formalism of
Lévy Walks. Simple counting processes are introduced and their properties are analyzed …

We analyze the statistical properties of a temporal point process driven by a confined
fractional Brownian motion. The event count distribution and power spectral density of this …

Recently the so-called Prabhakar generalization of the fractional Poisson counting process
attracted much interest for his flexibility to adapt to real world situations. In this renewal …

We construct admissible circulant Laplacian matrix functions as generators for strictly
increasing random walks on the integer line. These Laplacian matrix functions refer to a …

We introduce a new class of asymmetric random walks on the one-dimensional infinite
lattice. In this walk the direction of the jumps (positive or negative) is determined by a …

We consider a class of discrete-time random walks with directed unit steps on the integer
line. The direction of the steps is reversed at the time instants of events in a discrete-time …