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Earth System Dynamics An interactive open-access journal of the European Geosciences Union

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Earth Syst. Dynam., 8, 921-929, 2017
https://doi.org/10.5194/esd-8-921-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
16 Oct 2017
Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time
M. Levent Kavvas, Tongbi Tu, Ali Ercan, and James Polsinelli Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
Abstract. Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.

Citation: Kavvas, M. L., Tu, T., Ercan, A., and Polsinelli, J.: Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time, Earth Syst. Dynam., 8, 921-929, https://doi.org/10.5194/esd-8-921-2017, 2017.
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Short summary
A dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First a continuity equation for groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. An equation of water flux is also developed. The governing equation of transient groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained.
A dimensionally consistent governing equation of transient, saturated groundwater flow in...
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