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

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 formationsPresents useful aids for applied scientists and engineers seeking to solve complex problems that cannot be handled using constant fractional order derivativesProvides a real physical interpretation of operators relevant to groundwater flow problemsModels 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