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The Use of Fractional Order Derivative to Predict the Groundwater Flow

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  • Abdon Atangana
  • Necdet Bildik

Abstract

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.

Suggested Citation

  • Abdon Atangana & Necdet Bildik, 2013. "The Use of Fractional Order Derivative to Predict the Groundwater Flow," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, October.
    • Handle: RePEc:hin:jnlmpe:543026
    DOI: 10.1155/2013/543026
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    Cited by:

    1. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    2. Panda, Sumati Kumari & Vijayakumar, Velusamy, 2023. "Results on finite time stability of various fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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