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New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative

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Abstract

A novel definition of the concept of derivative with fractional order was introduced. To further enhance the mathematical model describing the flow of water within a leaky aquifer, we apply the novel derivative. The resulting equation was solved with three different methods. We presented some numerical simulations to show the efficiency of the used derivative.

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References

  • Atangana A (2016) On the new fractional derivative and application to nonlinear fisher's reaction-diffusion equation. Appl Math Comput 273:948–956

    Article  Google Scholar 

  • Barker JA (1988) A generalized radial flow model for hydraulic tests in fractured rock. Water Resour Res 24(10):1796–1804

    Article  Google Scholar 

  • Benson DA, Wheatcraft SW, Meerschaert MM (2000) Application of a fractional advection-dispersion equation. Water Resour Res 36(6):1403–1412

    Article  Google Scholar 

  • Berkowitz B, Cortis A, Dentz M, Scher H (2006) Modeling non-fickian transport in geological formations as a continuous time random walk. Rev Geophys vol. 44, no. 2, Article ID RG2003, pp 22-30

  • Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent, part II. Geophys J Int 13(5):529–539

    Article  Google Scholar 

  • Caputo M, Fabrizio M (2015) A new definition of fractional derivative without singular kernel. Prog Fract Differ Appl 1(2):73–85

    Google Scholar 

  • Hantush MS (1961a) Drawdown around a partially penetrating well. J Hyd Div Proc Am Soc Civil Eng vol. 87, no. HY4, pp 83–98

  • Hantush MS (1961b) Aquifer tests on partially penetrating wells. J Hyd Div Proc Am Soc Civil Eng vol. 87, no. HY5, pp 171–19

  • Losada J, Nieto JJ (2015) Properties of a new fractional derivative without singular kernel. Prog Fract Differ Appl 1(2):87–92

    Google Scholar 

  • Moench AF (1984) Double-porosity models for a fissured groundwater reservoir with fracture skin. Water Resour Res 20(7):831–846

    Article  Google Scholar 

  • Podlubny I (2002) Geometric and physical interpretation of fractional integration and fractional differentiation. Fractional Calc Appl Anal 5(4):367–386

    Google Scholar 

  • Ramey HJ (1982) Well-loss function and the skin effect: a review. In: Narasimhan TN (ed) Recent trends in hydrogeology. Geol Soc Am special paper 189, pp. 265–271

  • Rorabaugh MJ (1953) Graphical and theoretical analysis of step-drawdown test of artesian well. Proc Am Soc Civil Eng vol. 79, separate no. 362, 23pp

  • Theis CV (1935) The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Am Geophys Union Trans 16:519–524

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, 9300, Bloemfontein, South Africa

    Abdon Atangana & Badr Saad T. Alkahtani

Authors
  1. Abdon Atangana
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  2. Badr Saad T. Alkahtani
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Correspondence to Abdon Atangana.

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Atangana, A., Alkahtani, B.S.T. New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative. Arab J Geosci 9, 8 (2016). https://doi.org/10.1007/s12517-015-2060-8

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  • DOI: https://doi.org/10.1007/s12517-015-2060-8

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