Abstract
Fractional master equations containing fractional time derivatives of order 0<ω≤1 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 ψ(t) is obtained exactly as ψ(t)=(/C)(-/C), where (x) is the generalized Mittag-Leffler function. This waiting time distribution is singular both in the long time as well as in the short time limit.
- Received 28 October 1994
DOI:https://doi.org/10.1103/PhysRevE.51.R848
©1995 American Physical Society