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.
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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
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.