Para-Markov chains and related non-local equations
There is a well-established theory that links semi-Markov chains having Mittag-Leffler waiting times to time-fractional equations. We here go beyond the semi-Markov setting, by defining some non-Markovian chains whose waiting times, although marginally Mittag-Leffler, are assumed to be stochastically dependent. This creates a long memory tail in the evolution, unlike what happens for semi-Markov processes. As a special case of these chains, we study a particular counting process which extends the well-known fractional Poisson process, the last one having independent, Mittag-Leffler waiting times.
Authors
- Enrico Scalas (ORCID: https://orcid.org/0000-0002-1516-9285)
- Costantino Ricciuti (ORCID: https://orcid.org/0000-0001-7247-5302)
- Lorenzo Facciaroni (ORCID: https://orcid.org/0000-0003-3723-3927)
- Bruno Toaldo (ORCID: https://orcid.org/0000-0002-7570-3283)
Institutions
- University of Turin (IT)
- Sapienza University of Rome (IT)
Publication Details
- Journal
- Fractional Calculus and Applied Analysis
- Published
- 2025-04-02
- DOI
- https://doi.org/10.1007/s13540-025-00390-9
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Engineering and Physical Sciences Research Council
- Division of Mathematical Sciences