R. Hilfer, L. Anton
Physical Review E, Rapid Communication 51, R848 (1995)
https://doi.org/10.1103/PhysRevE.51.R848
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.
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