More generalized groundwater model with space‐time caputo Fabrizio fractional differentiation
Copyright policy )More generalized groundwater model with space‐time caputo Fabrizio fractional differentiation
We prove existence and uniqueness of the flow of water within a confined aquifer with fractional diffusion in space and fractional time derivative in the sense of Caputo‐Fabrizio using the classical contraction Banach theorem. We also propose the numerical approximation of the model using the Crank–Nicolson numerical scheme. To check the effectiveness of the model, stability analysis of the numerical scheme for the new model is presented.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1616–1627, 2017
- African Institute for Mathematical Sciences Cameroon
- University of the Free State South Africa
- African Institute for Mathematical Sciences South Africa
Flows in porous media; filtration; seepage, groundwater flow equation, Fractional partial differential equations, Finite difference methods applied to problems in fluid mechanics, Mathematics - Analysis of PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Caputo-Fabrizio fractional derivative, existence and uniqueness, Analysis of PDEs (math.AP)
Flows in porous media; filtration; seepage, groundwater flow equation, Fractional partial differential equations, Finite difference methods applied to problems in fluid mechanics, Mathematics - Analysis of PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Caputo-Fabrizio fractional derivative, existence and uniqueness, Analysis of PDEs (math.AP)
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