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The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1805–1812 | Cite as

Derivation of a fractional Boussinesq equation for modelling unconfined groundwater

  • B. Mehdinejadiani
  • H. Jafari
  • D. BaleanuEmail author
Regular Article

Abstract

In this manuscript, a fractional Boussinesq equation is obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Furthermore, it was assumed that the average thickness of the watery layer of an aquifer is constant, and the linear fractional Boussinesq equation was derived. Unlike classical Boussinesq equation, due to the non-locality property of fractional derivatives, the parameters of the fractional Boussinesq equation are constant and scale-invariant. In addition, the fractional Boussinesq equation has two various fractional orders of differentiation with respect to x and y that indicate the degree of heterogeneity in the x and y directions, respectively.

Keywords

Porous Medium Hydraulic Conductivity Control Volume Fractional Order European Physical Journal Special Topic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Department of Water Engineering, Faculty of AgricultureUniversity of KurdistanSanandajIran
  2. 2.Department of Mathematics, Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran
  3. 3.Department of Mathematics and Computer Sciences, Faculty of Art and SciencesCankaya UniversityAnkaraTurkey
  4. 4.Department of Chemical and Materials Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia
  5. 5.Institute of Space SciencesMagurele-BucharestRomania

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