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Published in

European Geosciences Union, Earth System Dynamics, 4(8), p. 921-929, 2017

DOI: 10.5194/esd-8-921-2017

European Geosciences Union, Earth System Dynamics Discussions, p. 1-15

DOI: 10.5194/esd-2017-47

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Fractional Governing Equations of Transient Groundwater Flow in Confined Aquifers with Multi-Fractional Dimensions in Fractional Time

Journal article published in 2017 by M. Levent Kavvas, Tongbi Tu ORCID, Ali Ercan ORCID, James Polsinelli
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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.