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

Date

2017-10-01

Author

Kavvas, M. Levent
Tu, Tongbi
Ercan, Ali
Polsinelli, James

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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 multifractional 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.

URI

https://hdl.handle.net/11511/100253

Journal

EARTH SYSTEM DYNAMICS

DOI

https://doi.org/10.5194/esd-8-921-2017

Collections

Department of Civil Engineering, Article

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Citation Formats

M. L. Kavvas, T. Tu, A. Ercan, and J. Polsinelli, “Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time,” EARTH SYSTEM DYNAMICS, vol. 8, no. 4, pp. 921–929, 2017, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100253.