Nonlocal and Fractional Operators

The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the applications in mathematical physics, as well as in probability. Numerical methods aimed to the solution of problems with fractional differential equations are also treated in the book. The contributions have been presented during the international workshop "Nonlocal and Fractional Operators", held in Sapienza University of Rome, in April 2019, and dedicated to the retirement of Prof. Renato Spigler (University Roma Tre). Therefore we also wish to dedicate this volume to this occasion, in order to celebrate his scientific contributions in the field of numerical analysis and fractional calculus. The book is suitable for mathematicians, physicists andapplied scientists interested in the various aspects of fractional calculus.

Luisa Beghin is Full Professor in Probability and Mathematical Statistics at Sapienza University of Rome (Italy). Her research interests include stochastic processes linked to fractional differential equations, Lévy processes, fractional and anomalous diffusions.

Roberto Garrappa is Associate Professor of Numerical Analysis at the University of Bari (Italy). His current research interests include numerical solution of ordinary and partial differential equations of fractional order and evaluation of special functions. He is the author of several numerical Matlab codes for fractional-order problems available in the MathWorks website.

Francesco Mainardi is retired Professor of Mathematical Physics from the University of Bologna, where he taught this course for more than 40 years. His research concerns several topics of applied mathematics, including  diffusion and wave problems, asymptotic methods, integraltransforms, special functions, fractional calculus and  non-Gaussian stochastic processes.