  We characterize a Hawkes point process with kernel proportional to the
probability density function of Mittag-Leffler random variables. This kernel
decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical
results can be proved, in particular for the expected intensity of the point
process and for the expected number of events of the counting process. These
analytical results are used to validate algorithms that numerically invert the
Laplace transform of the expected intensity as well as Monte Carlo simulations
of the process. Finally, Monte Carlo simulations are used to derive the full
distribution of the number of events. The algorithms used for this paper are
available at {\tt https://github.com/habyarimanacassien/Fractional-Hawkes}.
