On fractional diffusion and its relation with continuous time random walks

  • R. Hilfer
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 519)


Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is established between the fractional master equation and a separable continuous time random walk of the Montroll-Weiss type. The waiting time density can be expressed using a generalized Mittag-Leffler function. The first moment of the waiting density does not exist.


Continuous Time Master Equation Random Environment Infinitesimal Generator Fractional Diffusion 
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Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • R. Hilfer
    • 1
    • 2
  1. 1.Universität StuttgartICA-1Stuttgart
  2. 2.Institut für PhysikUniversität MainzMainzGermany

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