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.