Fractional Operators with Constant and Variable Order with Application to Geo-hydrology - 1st Edition - ISBN: 9780128096703, 9780128097960

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

1st Edition

Authors: Abdon Atangana
eBook ISBN: 9780128097960
Paperback ISBN: 9780128096703
Imprint: Academic Press
Published Date: 22nd September 2017
Page Count: 414
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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


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


No. of pages:
© Academic Press 2018
Academic Press
eBook ISBN:
Paperback ISBN:

About the Author

Abdon Atangana

Abdon Atangana’s serves as Professor at the University of Free State in Bloemfontein, South Africa. He specializes in applied mathematics, groundwater modeling, fractional calculus and their applications, methods for partial differential equations, methods for ordinary differential equations, iterations methods, asymptotic methods, perturbations methods, and numerical method for fractional differential equations, uncertainties analysis. He has participated in 18 international conferences, organized 6 special sections and symposium in international conference in Europe, Africa, Asia and USA, and has been invited as plenary speaker in 8 international conferences. He serves as editor for an international journal of applied mathematics and is the editor-in-chief for two international journals. He has authored more than 145 research papers in international accredited journals of mathematics and applied mathematics. His previous book, “Derivative with a New Parameter: Theory, Methods and Applications”, was published with Elsevier Sep-15, 2015.

Affiliations and Expertise

University of the Free State, Bloemfontein, South Africa

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