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More generalized groundwater model with space‐time caputo Fabrizio fractional differentiation
Author(s) -
Djida JeanDaniel,
Atangana Abdon
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22156
Subject(s) - mathematics , fractional calculus , uniqueness , partial differential equation , banach space , contraction mapping , stability (learning theory) , partial derivative , contraction principle , mathematical analysis , fixed point theorem , machine learning , computer science
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