Quantum dynamical maps provide suitable mathematical representation of quantum
evolutions. When representing quantum states by density operators, the evident …

This article discusses several definitions of the fractional Laplace operator L=—(—Δ) α/2 in
R d, also known as the Riesz fractional derivative operator; here α∈(0, 2) and d≥ 1. This is …

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 is a result of more than 10 years of research in the field of fractional calculus and
its application in stochastic processes and anomalous dynamics. The aim is to provide an …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

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 …

In this paper, we address the general fractional integrals and derivatives with the Sonine
kernels on the spaces of functions with an integrable singularity at the point zero. First, the …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

In this paper, we first address the general fractional integrals and derivatives with the Sonine
kernels that possess the integrable singularities of power function type at the point zero …

We develop a kind of fractional calculus and theory of relaxation and diffusion equations
associated with operators in the time variable, of the form (\mathbb D_ (k) u)(t)= d dt …