Fractional Klein-Kramers Equations: Subdiffusive and Superdiffusive Cases

  • Ralf Metzler
Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)


Brownian diffusion processes in phase space are described by the Klein-Kramers equation governing the time evolution of the probability density W(x, v, t) to find the test particle with velocity v at position x at time t. We here summarise generalisations of this equation to anomalous diffusion processes. These fractional Klein-Kramers equations describe either subdiffusive or superdiffusive processes.


Probability Density Function Test Particle Wait Time Distribution Continuous Time Random Walk Constant External Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Funding from the Academy of Finland within the FiDiPro scheme is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute for Physics and AstronomyUniversity of PotsdamPotsdam-GolmGermany
  2. 2.Physics DepartmentTampere University of TechnologyTampereFinland

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