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.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Dedication - p. v 6. Preface - p. xv 7. Acknowledgment - p. xvii 8. Chapter 1: Aquifers and Their Properties - p. xvii 9. Chapter 2: Principle of Groundwater Flow - p. 13 10. Chapter 3: Groundwater Pollution - p. 47 11. Chapter 4: Limitations of Groundwater Models With Local Derivative - p. 72 12. Chapter 5: Fractional Operators and Their Applications - p. 77 13. Chapter 6: Regularity of a General Parabolic Equation With Fractional Differentiation - p. 112 14. Chapter 7: Applications of Fractional Operators to Groundwater Models - p. 169 15. Chapter 8: Models of Groundwater Pollution With Fractional Operators - p. 209 16. Chapter 9: Fractional Variable Order Derivatives - p. 219 17. Chapter 10: Groundwater Flow Model in Self-similar Aquifer With Atangana–Baleanu Fractional Operators - p. 243 18. Chapter 11: Groundwater Flow Within a Fracture, Matrix Rock and Leaky Aquifers: Fractal Geometry - p. 261 19. Chapter 12: Modeling Groundwater Pollution With Variable Order Derivatives - p. 297 20. Chapter 13: Groundwater Recharge Model With Fractional Differentiation - p. 338 21. Chapter 14: Atangana Derivative With Memory and Application - p. 366 22. References - p. 381 23. Index - p. 391
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.
1. Cover image - p. iv 2. Title page - p. iv 3. Table of Contents - p. iv 4. Copyright - p. iv 5. Dedication - p. v 6. Preface - p. xv 7. Acknowledgment - p. xvii 8. Chapter 1: Aquifers and Their Properties - p. xvii 9. Chapter 2: Principle of Groundwater Flow - p. 13 10. Chapter 3: Groundwater Pollution - p. 47 11. Chapter 4: Limitations of Groundwater Models With Local Derivative - p. 72 12. Chapter 5: Fractional Operators and Their Applications - p. 77 13. Chapter 6: Regularity of a General Parabolic Equation With Fractional Differentiation - p. 112 14. Chapter 7: Applications of Fractional Operators to Groundwater Models - p. 169 15. Chapter 8: Models of Groundwater Pollution With Fractional Operators - p. 209 16. Chapter 9: Fractional Variable Order Derivatives - p. 219 17. Chapter 10: Groundwater Flow Model in Self-similar Aquifer With Atangana–Baleanu Fractional Operators - p. 243 18. Chapter 11: Groundwater Flow Within a Fracture, Matrix Rock and Leaky Aquifers: Fractal Geometry - p. 261 19. Chapter 12: Modeling Groundwater Pollution With Variable Order Derivatives - p. 297 20. Chapter 13: Groundwater Recharge Model With Fractional Differentiation - p. 338 21. Chapter 14: Atangana Derivative With Memory and Application - p. 366 22. References - p. 381 23. Index - p. 391
