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 …

In this survey we stress the importance of the higher transcendental Mittag-Leffler function in
the framework of the Fractional Calculus. We first start with the analytical properties of the …

A growing number of biological, soft, and active matter systems are observed to exhibit
normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a …

It is well established that a wide variety of phenomena in cellular and molecular biology
involve anomalous transport eg the statistics for the motility of cells and molecules are …

How does a systematic time-dependence of the diffusion coefficient D (t) affect the ergodic
and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this …

Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …

We study a heterogeneous diffusion process (HDP) with position-dependent diffusion
coefficient and Poissonian stochastic resetting. We find exact results for the mean squared …

Classical option pricing schemes assume that the value of a financial asset follows a
geometric Brownian motion (GBM). However, a growing body of studies suggest that a …

The emerging diffusive dynamics in many complex systems show a characteristic crossover
behaviour from anomalous to normal diffusion which is otherwise fitted by two independent …

In many dynamic processes, the fractional differential operators not only appear as discrete
fractional, but they also possess a continuous nature in a sense that their order is distributed …