Articles | Volume 11, issue 1
Earth Syst. Dynam., 11, 1–12, 2020
https://doi.org/10.5194/esd-11-1-2020
Earth Syst. Dynam., 11, 1–12, 2020
https://doi.org/10.5194/esd-11-1-2020

Research article 07 Jan 2020

Research article | 07 Jan 2020

Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

M. Levent Kavvas et al.

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Cited articles

Atangana, A.: Drawdown in prolate spheroidal–spherical coordinates obtained via Green's function and perturbation methods, Commun. Nonlinear Sci., 19, 1259–1269, 2014. 
Atangana, A. and Baleanu, D.: Modelling the advancement of the impurities and the melted oxygen concentration within the scope of fractional calculus, Int. J. Nonlin. Mech., 67, 278–284, 2014. 
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Short summary
After deriving a fractional continuity equation, a previously-developed equation for water flux in porous media was combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. As demonstrated in the numerical application, the orders of the fractional space and time derivatives modulate the speed of groundwater table evolution, slowing the process with the decrease in the powers of the fractional derivatives from 1.
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