Fractional master equations containing fractional time derivatives of order 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 as where 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.

PACS: 05.40.+j,05.60.+w,02.50+s