More generalized groundwater model with space‐time caputo Fabrizio fractional differentiation |
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| Authors: | Jean‐Daniel Djida Abdon Atangana |
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| Affiliation: | 1. African Institute for Mathematical Sciences (AIMS), Limbe Crystal Gardens, South West Region, Cameroon;2. Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa |
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| Abstract: | 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 |
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| Keywords: | groundwater flow equation Caputo– Fabrizio fractional derivative existence and uniqueness |
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