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.
- 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
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
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.