A mechanical picture of fractional-order Darcy equation

Luca Deseri, Massimiliano Zingales

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0 ≤ β≤1. If, instead, the physical properties of the media show a power-law increase from the control section, then flux is related to a fractional-order integral of order 0 ≤ β≤1. These two different behaviors may be related to different states of the mass flow across the porous media.

Original languageEnglish (US)
Pages (from-to)940-949
Number of pages10
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number3
StatePublished - Mar 1 2015


  • Anomalous diffusion
  • Anomalous scaling
  • Darcy equation
  • Fractional derivatives
  • Porous media

ASJC Scopus subject areas

  • Modeling and Simulation
  • Numerical Analysis
  • Applied Mathematics


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