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.

Numerous step-by-step tutorials help the reader to learn quickly A special chapter on next generation Flash prepares readers for the future Includes ten tips on how to protect flash sites from hackers

Auteur
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.

Résumé
"The book provides a survey of recent advancements in nonlocal and fractional models. It covers a vast range of topics involving nonlocal problems, from numerical methods, modeling, and applications to theoretical analysis. ... if you are a researcher working on nonlocal problems, or if you are a mathematician or applied scientist who is interested in learning the state-of-the-art theoretical and numerical developments in this field, this book will make a nice addition to your library." (Yue Yu, SIAM Review, Vol. 65 (3), 2023)

Contenu
G. Ascione et al., On the transient behavior of fractional M/M/queues.- G. Baumann, Sinc methods for Levy-Schroedinger equations.- A. Bazzani et al., Stochastic properties of colliding hard spheres in a non-equilibrium thermal bath.- A. Cardinali, Electromagnetic waves in non-local dielectric media: derivation of a fractional differential equation describing the wave dynamics.- A. Caserta et al., Some new exact results for non-linear space-fractional diffusivity equations.- C. Cesarano and A. Parmentier, A note on Hermite-Bernoulli polynomials.- J. Chen et al., A fractional Hawkes process.- A.Consiglio and F. Mainardi, Fractional diffusive waves in the Cauchy and signalling problems.- F. Ferrari, Some extension results for nonlocal operators and applications.- A. Lattanzi, The Pearcey equation: from the Salpeter relativistic equation to quasiparticles.- A. Maheshwari and R.Singh, Recent developments on fractional point processes.- A. Meoli, Some results on generalized accelerated motions driven by the telegraph process.- Á. Rodríguez-Rozas et al., The PDD method for solving linear, nonlinear and fractional PDEs problems.- V.Sposini et al., Fractional diffusion and medium heterogeneity: the case of the continuous time random walk.- M. Yamamoto, On time fractional derivatives in fractional Sobolev spaces and applications to fractional ordinary differential equations.