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Fractional Diffusion Equations and Anomalous Diffusion

$72.00 USD

  • Date Published: February 2018
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108695039

$ 72.00 USD
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About the Authors
  • 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.

    • Presents in a single text a historical and advanced point of view on diffusion problems and fractional calculus
    • Provides an introduction to fundamental problems of mathematical physics
    • The reader will have access to a new theoretical framework to interpret impedance spectroscopy data mainly in the low frequency region, where complex behaviour is usually found
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    Product details

    • Date Published: February 2018
    • format: Adobe eBook Reader
    • isbn: 9781108695039
    • contains: 92 b/w illus. 2 tables
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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.

  • Authors

    Luiz Roberto Evangelista, Universidade Estadual de Maringá, Brazil
    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, Universidade Estadual de Maringá, Brazil
    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.

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