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Fractional operators with constant and variable order with application to geo-hydrology /
Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equat...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London, England :
Academic Press,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology; Copyright; Contents; Preface; Acknowledgment; 1 Aquifers and Their Properties; 1.1 Introduction; 1.2 Classi cation of Aquifers; 1.3 Example of Some Aquifers in the World; 1.4 Some Identi ed Aquifer Properties; 2 Principle of Groundwater Flow; 2.1 Groundwater Within Geological Formations; 2.1.1 Groundwater Cycle; 2.1.2 Groundwater Overdraft; 2.1.3 Overview of Groundwater Within Subsurface; 2.2 Concept of Groundwater Flow Motion; 2.2.1 Darcy's Law and Its Application
- 2.2.2 Derivation of Darcy's Law2.3 Theis Model of Groundwater Flow; 2.3.1 Derivative of Theis Groundwater Flow Equation; 2.3.2 Derivation of Exact Solution; 2.3.3 Cooper and Jacob Approximation of Theis's Solution of Groundwater Flow Equation; 2.4 Groundwater Flow Within an Uncon ned Aquifer; 2.5 Groundwater Flow in a Deformable Aquifer; 2.5.1 Perturbation From Prolate Coordinates to Spherical Coordinates; 2.5.2 Derivation of Solution via Asymptotic Method; 2.6 Parallel Flow Model; 2.7 Uncertainties Analysis of Aquifer Parameters for Groundwater Flow Model; 2.7.1 Samples Generation
- 2.7.2 Evaluation of Uncertainties by Mean of Statistic Formulas Parameters uncertainties evaluation of groundwater ow equation; 3 Groundwater Pollution; 3.1 History of Groundwater Pollution: Love Canal Disaster; 3.1.1 Love Canal Disaster; 3.1.2 Construction of the 93rd Street School and the 99th Street School; 3.1.3 Health Problems and Site Cleanup of Love Canal; 3.2 Source of Pollution; 3.3 Type of Pollution; 3.4 Heath Problems Caused by Groundwater Pollution; 3.5 Convection Dispersion Model; 3.5.1 Derivation of the Mathematical Model; 3.5.2 Derivation of Exact Solution
- 3.6 Groundwater Remediation: Techniques and Actions3.6.1 Remediation Technique; Risk assessment; 3.6.2 Remediation Action; Some techniques for groundwater remediation; 3.7 Sensibility Analysis of Model Parameters; 3.7.1 Some Commonly Used Methods for Sensitivity Analysis; 3.7.2 Limitations of Sensibility Analysis Methods; 3.8 Problems of Transboundary Aquifers; 4 Limitations of Groundwater Models With Local Derivative; 4.1 Limitations of Groundwater Flow Model; 4.2 Limitations of Groundwater Convection Dispersion Model; 5 Fractional Operators and Their Applications
- 5.1 Introduction to the Concept of Fractional Calculus5.2 Riemann-Liouville Type; 5.2.1 Some Useful Properties; 5.3 Caputo Type; 5.4 Beta-Type; 5.5 Fractal Type; 5.6 Caputo-Fabrizio Type; 5.7 Caputo-Fabrizio in Riemann-Liouville Sense; 5.8 Atangana-Baleanu Derivatives With Fractional Order; 5.8.1 Motivations and De nitions With New Kernel; 5.8.2 Properties of Atangana-Baleanu Derivatives With Fractional Order; 5.8.3 Relation With Integral Transforms; 5.9 Physical Interpretation of Fractional Derivatives; 5.10 Advantages and Limitations; 5.10.1 Advantages of Fractional Derivatives