Earth System Dynamics
Earth System Dynamics
ESD
Articles | Volume 11, issue 1
Articles | Volume 11, issue 1
https://doi.org/10.5194/esd-11-1-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-11-1-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 11, issue 1
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, Tongbi Tu, Ali Ercan, and James Polsinelli

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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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