Fractional Diffusion Equations and Anomalous Diffusion

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Ervin Kaminski Lenzi Luiz Roberto EvangelistaCambridge University Press, 2/28/2018EAN 9781107143555, ISBN10: 1107143551Hardcover, 395 pages, 25.5 x 17.9 x 2 cmLanguage: EnglishAnom alous 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.Preface1. Mathematical preliminaries2. A survey of the fractional calculus3. From normal to anomalous diffusion4. Fractional diffusion equationselementary applications5. Fractional diffusion equationssurface effects6. Fractional nonlinear diffusion equation7. Anomalous diffusionanisotropic case8. Fractional Schrödinger equations9. Anomalous diffusion and impedance spectroscopy10. The Poisson–Nernst–Planck anomalous (PNPA) modelsReferencesIndex. Show more