In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show tha...

We study the combined effects of noise and detector sensitivity on a dynamical process that generates intermittent events mimicking the behavior of complex systems. By varying the sensitivity level of the detector we move between two forms of complexity, from inverse power law to Mittag-Leffler interevent time survival probabilities. Here fluctuations fight against complexity, causing an expone...

In this paper, a mathematical model containing two-parameter Mittag-Leffler function in its definition is proposed to be used for the first time to fit the relation between unemployment rate and inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a powe...

A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.

In this communique, we present a new family of Nussbaum functions expressed by Mittag–Leffler functions under certain conditions. © 2009 Elsevier Ltd. All rights reserved.

Since Gösta Magus Mittag-Leffler introduced the so-called function in 1903 and studied its features five subsequent notes, passing first half of 20th century during which majority scientists remained almost unaware function, various extensions (referred to as type functions) have been researched applied a wide range problems physics, biology, chemistry, engineering. In context fractional calcul...