Fractional Diffusion Equations and Anomalous Diffusion

Presents a unified treatment of anomalous diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.

Luiz Roberto Evangelista (Author), Ervin Kaminski Lenzi (Author)

9781107143555, Cambridge University Press

Hardback, published 25 January 2018

358 pages, 92 b/w illus. 2 tables
25.5 x 17.9 x 2 cm, 0.87 kg

'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

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.

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.

Subject Areas: Chemistry [PN], Statistical physics [PHS], Mathematical modelling [PBWH]