Screen LibraryFractional diffusion equations and anomalous diffusion /
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| Main Authors: | |
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| Group Author: | |
| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge, United Kingdom : |
| Publication Dates: | 2018. |
| Literature type: | Book |
| Language: | English |
| Subjects: | |
| Carrier Form: | xiii, 345 pages : illustrations ; 26 cm |
| Bibliography: | Includes bibliographical references (pages 323-340) and index. |
| ISBN: |
9781107143555 (hardcover : alkaline paper) : 1107143551 (hardcover : alkaline paper) |
| Index Number: | QA377 |
| CLC: | O175.2 |
| Call Number: | O175.2/E923 |
| Contents: |
Mathematical Preliminaries -- Integral Transforms -- Special Functions of Fractional Calculus -- Integral Transforms of Special Functions -- A Survey of Fractional Calculus -- The Origins of Fractional Calculus -- The Grunwald -- Letnikov Operator -- The Caputo Operator -- The Riesz -- Weyl Operator -- Integral Transforms of Fractional Operators -- A Generalised Fourier Transform -- From Normal to Anomalous Diffusion -- Historical Perspectives on Diffusion Problems -- Continuous-Time Random Walk -- Diffusion Equation -- Fractional Diffusion Equations -- Fractional Time Derivative: Simple Situations -- Fractional Spatial Derivative: Simple Situations -- Sorption and Desorption Processes -- Reaction Terms -- Reaction and CTRW Formalism -- ID and 2D Cases: Different Diffusive Regimes -- 3D Case: External Force and Reaction Term -- Reaction on a Solid Surface: Anomalous Mass Transfer -- Heterogeneous Media and Transport through a Membrane -- Fractional Nonlinear Diffusion Equations -- Nonlinear Diffusion Equations -- Nonlinear Diffusion Equations: Intermittent Motion -- Fractional Spatial Derivatives -- d-Dimensional Fractional Diffusion Equations -- Anomalous Diffusion -- The Adsorption -- Desorption Process in Anisotropic Media -- Fractional Diffusion Equations in Anisotropic Media -- The Comb Model -- Fractional Schrodinger Equations -- The Schrodinger Equation and Anomalous Behaviour -- Time-Dependent Solutions -- CTRW and the Fractional Schrodinger Equation -- Memory and Nonlocal Effects -- Nonlocal Effects on the Energy Spectra -- Anomalous Diffusion and Impedance Spectroscopy -- Impedance Spectroscopy: Preliminaries -- The PNP Time Fractional Model -- Anomalous Diffusion and Memory Effects -- Anomalous Interfacial Conditions -- The Poisson -- Nernst -- Planck Anomalous Models -- PNPA Models and Equivalent Circuits -- PNPA Models: A Framework. |