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Fractional diffusion equations and anomalous diffusion

Author: L R Evangelista; Ervin Kaminski Lenzi
Publisher: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018. ©20 ©2018
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

A contemporary treatment of anomalous diffusion, this book examines the recent literature in the field and covers a rich class of problems in which surface effects are important, offering detailed  Read more...

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Additional Physical Format: ebook version :
Document Type: Book
All Authors / Contributors: L R Evangelista; Ervin Kaminski Lenzi
ISBN: 9781107143555 1107143551
OCLC Number: 1002043888
Description: xiii, 345 pages ; 26 cm
Contents: 1. Mathematical Preliminaries --
1.1. Integral Transforms --
1.2. Special Functions of Fractional Calculus --
1.3. Integral Transforms of Special Functions --
2. A Survey of Fractional Calculus --
2.1. The Origins of Fractional Calculus --
2.2. The Grunwald --
Letnikov Operator --
2.3. The Caputo Operator --
2.4. The Riesz --
Weyl Operator --
2.5. Integral Transforms of Fractional Operators --
2.6. A Generalised Fourier Transform --
3. From Normal to Anomalous Diffusion --
3.1. Historical Perspectives on Diffusion Problems --
3.2. Continuous-Time Random Walk --
3.3. Diffusion Equation --
4. Fractional Diffusion Equations --
4.1. Fractional Time Derivative: Simple Situations --
4.2. Fractional Spatial Derivative: Simple Situations --
4.3. Sorption and Desorption Processes --
4.4. Reaction Terms --
4.5. Reaction and CTRW Formalism --
5 Fractional Diffusion Equations --
5.1. ID and 2D Cases: Different Diffusive Regimes --
5.2. 3D Case: External Force and Reaction Term --
5.3. Reaction on a Solid Surface: Anomalous Mass Transfer --
5.4. Heterogeneous Media and Transport through a Membrane --
6. Fractional Nonlinear Diffusion Equations --
6.1. Nonlinear Diffusion Equations --
6.2. Nonlinear Diffusion Equations: Intermittent Motion --
6.3. Fractional Spatial Derivatives --
6.4. d-Dimensional Fractional Diffusion Equations --
7. Anomalous Diffusion --
7.1. The Adsorption --
Desorption Process in Anisotropic Media --
7.2. Fractional Diffusion Equations in Anisotropic Media --
7.3. The Comb Model --
8. Fractional Schrodinger Equations --
8.1. The Schrodinger Equation and Anomalous Behaviour --
8.2. Time-Dependent Solutions --
8.3. CTRW and the Fractional Schrodinger Equation --
8.4. Memory and Nonlocal Effects --
8.5 Nonlocal Effects on the Energy Spectra --
9. Anomalous Diffusion and Impedance Spectroscopy --
9.1. Impedance Spectroscopy: Preliminaries --
9.2. The PNP Time Fractional Model --
9.3. Anomalous Diffusion and Memory Effects --
9.4. Anomalous Interfacial Conditions --
10. The Poisson --
Nernst --
Planck Anomalous Models --
10.1. PNPA Models and Equivalent Circuits --
10.2. PNPA Models: A Framework.
Responsibility: Luiz Roberto Evangelista, Ervin Kaminski Lenzi.

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