2013/01/01 by Abdon Atangana, Necdet Bıldık · 1 citation
Mathematics · Physics and Astronomy · Computer Science · #Fractional Differential Equations Solutions #Model Reduction and Neural Networks #Numerical Methods and Algorithms #Groundwater flow equation #Laplace transform #Hydraulic head #Groundwater flow #Borehole #Groundwater #Fractional calculus #Exponential function #Mathematics #Flow (mathematics) #Aquifer #Applied mathematics #Mathematical analysis #Geotechnical engineering #Geology #Geometry
paper · pdf · doi:10.1155/2013/543026
openalex publication_date 2013/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.