ABSTRACT

This book is an unique integrated treatise, on the concepts of fractional calculus as models with applications in hydrology, soil science and geomechanics. The models are primarily fractional partial differential equations (fPDEs), and in limited cases, fractional differential equations (fDEs). It develops and applies relevant fPDEs and fDEs mainly to water flow and solute transport in porous media and overland, and in some cases, to concurrent flow and energy transfer. It is an integrated resource with theory and applications for those interested in hydrology, hydraulics and fluid mechanics. The self-contained book summaries the fundamentals for porous media and essential mathematics with extensive references supporting the development of the model and applications.

chapter Chapter 2|39 pages

Mathematical Preliminaries

chapter Chapter 4|32 pages

Transition from Classical Diffusion to Anomalous Diffusion

The Evolution of Concepts and Ideas

chapter Chapter 11|17 pages

Fractional Partial Differential Equations and their Applications to Poroviscoelastic Media and Geomechanics

Re-familiarization and Introduction for Hydrologists and Soil Scientists