Nonlocal and Fractional Operators

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.

• 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.

“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)