On a generalized diffusion equation arising in petroleum engineering

Suliman Al-Homidan, Ryad Ghanam, Nasser Eddine Tatar

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2 Citations (Scopus)

Abstract

In this work we investigate a model which describes diffusion in petroleum engineering. The original model, which already generalizes the standard one (usual diffusion equation) to a non-local model taking into account the memory effects, is here further extended to cope with many other different possible situations. Namely, we consider the Hilfer fractional derivative which by its nature interpolates the Riemann-Liouville fractional derivative and the Caputo fractional derivative (the one that has been studied previously). At the same time, this kind of derivative provides us with a whole range of other types of fractional derivatives. We treat both the Neumann boundary conditions case and the Dirichlet boundary conditions case and find explicit solutions. In addition to that, we also discuss the case of an infinite reservoir.

Original languageEnglish
Article number349
JournalAdvances in Difference Equations
Volume2013
DOIs
Publication statusPublished - Dec 2013
Externally publishedYes

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ASJC Scopus subject areas

  • Applied Mathematics
  • Algebra and Number Theory
  • Analysis

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