  Fractional Poisson processes, a rapidly growing area of non-Markovian
stochastic processes, are useful in statistics to describe data from counting
processes when waiting times are not exponentially distributed. We show that
the fractional Kolmogorov-Feller equations for the probabilities at time t can
be representated by an infinite linear system of ordinary differential
equations of first order in a transformed time variable. These new equations
resemble a linear version of the discrete coagulation-fragmentation equations,
well-known from the non-equilibrium theory of gelation, cluster-dynamics and
phase transitions in physics and chemistry.
