Fractional Diffusion Equations and Anomalous Diffusion

AvLuiz Roberto Evangelista,Ervin Kaminski Lenzi

Inbunden, Engelska, 2018

1 012 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2018-01-25
Mått:179 x 255 x 20 mm
Vikt:870 g
Format:Inbunden
Språk:Engelska
Antal sidor:358
Förlag:Cambridge University Press
ISBN:9781107143555

Utforska kategorier

Tillämpad matematik inom Naturvetenskap och teknik
Kemi inom Naturvetenskap och teknik
Fysik inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'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

Innehållsförteckning

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.