Screen LibraryFractional 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...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
Academic Press,
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| Publisher Address: | London, England : |
| Publication Dates: | 2018. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
https://www.sciencedirect.com/science/book/9780128096703 |
| Summary: |
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 equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author's analyses, the book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution. |
| Carrier Form: | 1 online resource (416 pages) : illustrations (some color), tables |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: |
0128097965 9780128097960 |
| Index Number: | GB1003 |
| CLC: | P641 |
| Contents: |
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 |