Fractional Operators with Constant and Variable Order with Application to Geo-hydrology
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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
Readership
Researchers and practitioners interested in groundwater modeling and remediation from applied mathematics and geo-hydrology backgrounds
Table of Contents
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
Product details
- No. of pages: 414
- Language: English
- Copyright: © Academic Press 2017
- Published: September 19, 2017
- Imprint: Academic Press
- eBook ISBN: 9780128097960
- Paperback ISBN: 9780128096703
About the Author
Abdon Atangana
Dr. Abdon 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 was included in the 2019 (Maths), 2020 (Cross-field) and the 2021 (Maths) Clarivate Web of Science lists of the World's top 1% scientists, and he was awarded The World Academy of Sciences (TWAS) inaugural Mohammed A. Hamdan award for contributions to science in developing countries. In 2018 Dr. Atangana was elected as a member of the African Academy of Sciences and in 2021 a member of The World Academy of Sciences. He also ranked number one in the world in mathematics, number 186 in the world in all fields, and number one in Africa in all fields, according to the Stanford University list of top 2% scientists in the world. He was one of the first recipients of the Obada Award in 2018. Dr. Atangana published a paper that was ranked by Clarivate in 2017 as the most cited mathematics paper in the world. Dr. Atangana serves as an editor for 20 international journals, lead guest editor for 10 journals, and is also a reviewer of more than 200 international accredited journals. His research interests include methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Dr. Atangana is a pioneer in research on fractional calculus with non-local and non-singular kernels popular in applied mathematics today. He is the author of numerous books, including Integral Transforms and Engineering: Theory, Methods, and Applications, Taylor and Francis/CRC Press; Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling, Taylor and Francis/CRC Press; Numerical Methods for Fractional Differentiation, Springer; Fractional Stochastic Differential Equations, Springer; Fractional Order Analysis, Wiley; Applications of Fractional Calculus to Modeling in Dynamics and Chaos, Taylor and Francis/CRC Press; Fractional Operators with Constant and Variable Order with Application to Geo-hydrology, Elsevier/Academic Press; Derivative with a New Parameter: Theory, Methods, and Applications, Elsevier/Academic Press; and New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications, Elsevier/Academic Press; among others.
Affiliations and Expertise
Academic Head of Department and Professor of Applied Mathematics, University of the Free State, Bloemfontein, South Africa
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