I summarise results of three papers [1,2,3] on a fractional Hawkes process with kernel proportional to the probability density function of Mittag-Leffler random variables. This is joint work with Jane A. Aduda, Maggie Chen, the late Alan G. Hawkes, Cassien Habyarimana, and Federico Polito. The code used to generate simulations and figures is freely available from https://github.com/habyarimanacassien/Fractional-Hawkes.

1. Chen, J., Hawkes, A.G., Scalas, E.: A Fractional Hawkes Process, In: Beghin, L., Mainardi, F., Garrappa, R. (eds.) Nonlocal and Fractional Operators. SEMA SIMAI Springer Series, vol 26. Springer, (2021). 2. Habyarimana C., Aduda J.A., Scalas, E., Chen, J., Hawkes A.G., Polito F.: A fractional Hawkes process II: Further characterization of the process. Physica A 615, 128596, (2023). 3. Habyarimana C., Aduda J.A., Scalas E.: Parameter estimation for the fractional Hawkes process. Journal of Agricultural, Biological and Environmental Statistics, (2024). https://doi.org/10.1007/s13253-024-00663-5.