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# Fractional Operators with Constant and Variable Order with Application to Geo-hydrology

## 1st Edition

Author:
eBook ISBN: 9780128097960
Paperback ISBN: 9780128096703
Published Date: 19th September 2017
Page Count: 414
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## Description

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.

## Key Features

• Proposes new aquifer derivatives for leaky, confined and unconfined formations
• Presents useful aids for applied scientists and engineers seeking to solve complex problems that cannot be handled using constant fractional order derivatives
• Provides a real physical interpretation of operators relevant to groundwater flow problems
• Models both fractional and variable order derivatives, presented together with uncertainties analysis

Researchers and practitioners interested in groundwater modeling and remediation from applied mathematics and geo-hydrology backgrounds

1. Aquifers and their properties
2. Principle of groundwater flow
3. Groundwater pollution
4. Limitations of groundwater models with local derivative
5. Fractional operators and their applications
6. Regularity of a general parabolic equation with fractional differentiation
7. Applications of fractional operators to groundwater models
8. Models of groundwater pollution with fractional operators
9. Fractional variable order derivatives
10. Groundwater fractal flow model with Atangana-Baleanu fractional operators
11. Growndwater flowing within a fracture and matrix rock
12. Modeling groundwater pollution with variable order derivatives
13. Groundwater recharge model with fractional differentiation
14. Atangana derivative with memory and application

## Details

No. of pages:
414
Language:
English
Published:
19th September 2017
Imprint:
eBook ISBN:
9780128097960
Paperback ISBN:
9780128096703

## About the Author

### Abdon Atangana

Dr. Atangana is Academic Head of Department and Professor of Applied Mathematics at the University of the Free State, Bloemfontein, Republic of South Africa. He obtained his honours and master’s degrees from the Department of Applied Mathematics at the UFS with distinction. He obtained his PhD in applied mathematics from the Institute for Groundwater Studies. He serves as an editor for 20 international journals and lead guest editor in 10 journals and is also a reviewer of more than 200 international accredited journals. His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Prof Atangana is the founder of fractional calculus with non-local and non-singular kernels popular in applied mathematics today. Since 2013, he has published in 250 international accredited journals of applied mathematics, applied physics, geo-hydrology and biomathematics. He is also the single author of two books in Academic Press Elsevier and a co-author of a book published in springer and author of more than 20 chapters in books. He has graduated 7 PhD and 20 masters students, and 6 postdoc fellows.

### Affiliations and Expertise

Academic Head of Department and Professor of Applied Mathematics, University of the Free State, Bloemfontein, South Africa

## Reviews

"This book provides a physical review of fractional operators, fractional-order operators, and uncertain derivatives within the context of 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 noninteger-order derivatives. The book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution." --Zentralblatt MATH