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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) = (t ω−1 /C)E ω,ω (−t ω /C) where E ω,ω (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. Contents 3 Appendix A. Definition of H-functions 4 References 5

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