Numerical approach to the fractional Klein-Kramers equation.

@article{Magdziarz2007NumericalAT,
  title={Numerical approach to the fractional Klein-Kramers equation.},
  author={Marcin Magdziarz and Aleksander Weron},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2007},
  volume={76 6 Pt 2},
  pages={
          066708
        }
}
Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation. The structure of the introduced process agrees with the two-stage scenario underlying the anomalous diffusion mechanism, in which trapping events are… CONTINUE READING

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Integrals and Derivatives of the Fractional Order and Some of Their Applications  Gordon and Breach , Amsterdam , 1993  .  9  R . Metzler and I . M . Sokolov

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