| Description |
1 online resource illustrations (black and white, and colour) |
| Contents |
Cover -- Title Page -- Copyright Page -- Foreword -- Preface -- Table of Contents -- 1. Application of Fractional Calculus in Water Flow and Related Processes -- 1. Overview -- 2. Objectives of This Book -- 3. A Brief Description of Key Concepts -- 3.1 Evolution of Mathematical Models in Hydrology, Hydraulics, Soil Science, and Geomechanics Based on Fractional Calculus -- 3.2 Developments in the Theory and Methodologies for Poroelasticity -- 3.3 Hydrology, Hydraulics, Soil Science, Geomechanics (Soil Mechanics) and Their Relevance to Environmental Issues -- 4. Notation in the Book |
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2. Mathematical Preliminaries -- 1. Introduction -- 1.1 Basic Concepts, Definitions and Classification of Differential Equations -- 1.2 Major Types of PDEs Used in Flow in Porous Media, Hydrology, Soil Science and Geomechanics -- 2. Integral Transforms -- 2.1 Fourier Transform and Inverse Fourier Transform -- 2.2 Laplace Transform and Inverse Laplace Transform -- 3. Asymptotic Analysis -- 4. Special Functions -- 4.1 Gamma Function and Related Functions -- 4.2 Incomplete Gamma Function -- 4.3 Beta Function -- 4.4 Mittag-Leffler Function and Related Functions |
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4.5 Wright Function and Generalized Wright Function -- 5. Fundamental Solution, Green Function, Delta Functions and Generalized Functions -- 5.1 Historical Development of the Ideas -- 5.2 Dirac Delta Function, S Function and the Heaviside Step Function -- 5.3 Heaviside Step Function and Its Relationship with Dirac Delta Function -- 5.4 Kronecker's Delta Function -- 5.5 Generalized Function and Its Applications in fPDEs -- 6. Fractional Integration and Fractional Differentiation -- 6.1 Riemann-Liouville and Liouville Fractional Integrals |
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6.2 Riemann-Liouville and Liouville Fractional Derivatives -- 6.3 Caputo Fractional Derivatives -- 6.4 Symmetric Fractional Derivatives (SFDs) -- 7. Summary -- Appendices -- Appendix 2.1: Laplace Transforms of Special Functions in Fractional Calculus and Related Topics -- Appendix 2.2: Additional Properties of the Dirac Delta Function -- Appendix 2.3: Hypergeometric Series as the Generating Function for Other Special Functions -- Appendix 2.4: Some Special Functions Expressed as Fractional Derivatives -- 3. Essential Properties of Soils and Aquifers as Porous Media |
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1. Introduction: Soils and Aquifers as Porous Media -- 2. Descriptive Concepts and Definitions of Soils and Aquifers -- 2.1 Pores and Porosity, and Related Concepts -- 2.2 Void Ratio -- 2.3 Density of Solids (Mean Particle Density) -- 2.4 Wet Bulk Density and Dry Bulk Density -- 2.5 Gravitational Water Content and Volumetric Water Content -- 2.6 Degree of Saturation -- 2.7 Other Identities and Their Relationships -- 2.8 Material Coordinate for Quantifying Swelling-shrinking Soils -- 3. Fundamental Equations of Flow in Soils and Aquifers -- 3.1 Introduction |
| Summary |
"This book presents the most relevant concepts and findings in fractional calculus (FC), fractional differential equations (FDEs) and fractional partial differentia equations (FPDEs) and their applications in soil physics, groundwater hydrology, soil mechanics, irrigation and drainage engineering, earth and environmental sciences and environmental engineering. Readers of this book will be postgraduates, senior undergraduates, academics, researchers and other professionals in these fields. A reader from the above fields will find the most relevant materials necessary for the initial study and immediate applications of the concepts and models with examples. It is the first book in soil science, hydrology and soil mechanics"-- Provided by publisher |
| Subject |
Hydrology -- Mathematical models
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Soil science -- Mathematical models
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Soil mechanics -- Mathematical models
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Rock mechanics -- Mathematical models
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Fractional calculus.
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Fractional calculus.
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Hydrology -- Mathematical models.
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Rock mechanics -- Mathematical models.
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Soil mechanics -- Mathematical models.
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Soil science -- Mathematical models.
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| Form |
Electronic book
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| ISBN |
9781351032414 |
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1351032410 |
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