Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad
distribution of time-scales present in their complex internal structure. A promising tool to …

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 generalized fractional derivative (GFD) definition is proposed in this work. For a
differentiable function expanded by a Taylor series, we show that DαDβf (t)= Dα+ βf (t); 0< …

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

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 …

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 …

Fractional-order Systems and Controls details the use of fractional calculus (calculus of non-
integer order) in the description and modeling of systems, and in a range of control design …

In the present note, first we have established Hermite–Hadamard's inequalities for fractional
integrals. Second, an integral identity and some Hermite–Hadamard type integral …

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 …