Fractional Diffusion Equations and 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.
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 Schroedinger equations; 9. Anomalous diffusion and impedance spectroscopy;
10. The Poisson-Nernst-Planck anomalous (PNPA) models; References; Index.
Presents a unified treatment of anomalous
diffusion problems using fractional calculus in a wide range of applications across scientific and technological disciplines.