Articles | Volume 8, issue 4
https://doi.org/10.5194/esd-8-921-2017
https://doi.org/10.5194/esd-8-921-2017
Research article
 | 
16 Oct 2017
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

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.

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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.
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