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 …

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 …

Recently fractional differential operators with non-index law properties have being
recognized to have brought new weapons to accurately model real world problems …

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

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra
integral equations (VIEs), ranging from Volterra's fundamental contributions and the …

Computers and electronics play an enormous role in today's society, impacting everything
from communication and medicine to science. The development of computer-related …

This chapter is devoted to time-and space-nonlocal generalizations of the standard Fourier
law, the corresponding generalizations of the classical heat conduction equation and …

This book contains mathematical preliminaries in which basic definitions of fractional
derivatives and spaces are presented. The central part of the book contains various …

Up to now we have introduced a fractional derivative definition for special simple function
classes. In the following section we will present common generalizations for arbitrary …

Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …