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Fractional Fokker-Planck Equation

Author

Listed:
  • Gerd Baumann

    (Mathematics Department, German University in Cairo, New Cairo City 11835, Egypt
    University of Ulm, D-89069 Ulm, Germany)

  • Frank Stenger

    (University of Utah, Salt Lake City, UT 84112, USA)

Abstract

We shall discuss the numerical solution of the Cauchy problem for the fully fractional Fokker-Planck (fFP) equation in connection with Sinc convolution methods. The numerical approximation is based on Caputo and Riesz-Feller fractional derivatives. The use of the transfer function in Laplace and Fourier spaces in connection with Sinc convolutions allow to find exponentially converging computing schemes. Examples using different initial conditions demonstrate the effective computations with a small number of grid points on an infinite spatial domain.

Suggested Citation

  • Gerd Baumann & Frank Stenger, 2017. "Fractional Fokker-Planck Equation," Mathematics, MDPI, vol. 5(1), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:1:p:12-:d:90059
    as

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    References listed on IDEAS

    as
    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    2. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
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