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 …

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any
arbitrary real or complex order) has gained considerable popularity and importance during …

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of
the special functions with respect to another function, and the integro-differential operators …

In this paper we introduce a new fractional derivative with respect to another function the so-
called ψ-Hilfer fractional derivative. We discuss some properties and important results of the …

Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly
established fractional-order calculus operators involving singular and non-singular kernels …

This monograph is an invitation both to the interested scientists and the engineers. It
presents a thorough introduction to the recent results of local fractional calculus. It is also …

Many possible definitions have been proposed for fractional derivatives and integrals,
starting from the classical Riemann–Liouville formula and its generalisations and modifying …

We consider an initial value problem for a class of nonlinear fractional differential equations
involving Hilfer fractional derivative. We prove existence and uniqueness of global solutions …

Motivated essentially by the success of the applications of the Mittag‐Leffler functions in
many areas of science and engineering, the authors present, in a unified manner, a detailed …