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An Implementation Solution for Fractional Partial Differential Equations

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  • Nicolas Bertrand
  • Jocelyn Sabatier
  • Olivier Briat
  • Jean-Michel Vinassa

Abstract

The link between fractional differentiation and diffusion equation is used in this paper to propose a solution for the implementation of fractional diffusion equations. These equations permit us to take into account species anomalous diffusion at electrochemical interfaces, thus permitting an accurate modeling of batteries, ultracapacitors, and fuel cells. However, fractional diffusion equations are not addressed in most commercial software dedicated to partial differential equations simulation. The proposed solution is evaluated in an example.

Suggested Citation

  • Nicolas Bertrand & Jocelyn Sabatier & Olivier Briat & Jean-Michel Vinassa, 2013. "An Implementation Solution for Fractional Partial Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, March.
    • Handle: RePEc:hin:jnlmpe:795651
    DOI: 10.1155/2013/795651
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