Fractional Diffusion Equations and Anomalous Diffusion

by Luiz Roberto Evangelista, Ervin Kaminski Lenzi

Overview

Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.

Product Details

ISBN-13:	9781107143555
Publisher:	Cambridge University Press
Publication date:	01/25/2018
Pages:	358
Product dimensions:	7.05(w) x 10.04(h) x 0.79(d)

About the Author

Luiz Roberto Evangelista is Professor of Theoretical Physics at the Universidade Estadual de Maringá, Brazil. His research interests lie in complex fluids, complex systems, and history of physics, and include mathematical physics of liquid crystals, diffusion problems, and adsorption-desorption phenomena.

Ervin Kaminski Lenzi is Associate Professor at the Universidade Estadual de Ponta Grossa, Brazil. His research interests are in complex systems and stochastic processes, and include anomalous diffusion processes, usual and fractional diffusion equations, and modern boundary value problems with applications in liquid-crystalline systems and impedance spectroscopy.

Table of Contents

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Editorial Reviews

'This is a very advanced book … The aim of the book is to disseminate recent results in the field. I would recommend it to people with a specialised interest in anomalous diffusion.' John Bartlett, Mathematics Today

‘This book is devoted to the study of anomalous diffusion phenomena in order to provide an updated literature on this topic as well as to discuss a wide class of problems where this process occurs.’ Raffaella Servadei, ZB Math Reviews

From the Publisher