Fractional Calculus Fractional Time Random Walks Stochastic Processes Theory of Time

Fractional Master Equations and Fractal Time Random Walks

R. Hilfer, L. Anton

Physical Review E, Rapid Communication 51, R848 (1995)

submitted on
Friday, October 28, 1994

Fractional master equations containing fractional time derivatives of order less than one are introduced on the basis of a recent classification of time generators in ergodic theory. It is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks. The corresponding waiting time density is obtained exactly in terms of the generalized Mittag-Leffler function. This waiting time distribution is singular both in the long time as well as in the short time limit.

For more information see