The Use of Fractional Order Derivative to Predict the Groundwater Flow
By Abdon Atangana, Necdet Bildik. 2013
83 citations recorded by the source corpus.
The aim of this work was to convert the Thiem and the Theis groundwater flow equation to the time-fractional groundwater flow model. We first derived the analytical solution of the Theim time-fractional groundwater flow equation in terms of the generalized Wright function. We presented some properties of the Laplace-Carson transform. We derived the analytical solution of the Theis-time-fractional groundwater flow equation (TFGFE) via the Laplace-Carson transform method. We introduced the generalized exponential integral, as solution of the TFGFE. This solution is in perfect agreement with the data observed from the pumping test performed by the Institute for Groundwater Study on one of its borehole settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes.
Subfields: Computational Theory and Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/659041403e8eb439216b0a02e764d05d378dba54
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Citations in the corpus
- Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer (2016, background): “Therefore the new model of groundwater flow within subsurface geological formation called unconfined aquifer is give as [3, 5, 7, 12, 13]:”