Work

Para-Markov chains and related non-local equations

Year: 2025

Type: article

Abstract: 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.

Source: Fractional Calculus and Applied Analysis

DOI: 10.1007/s13540-025-00390-9

Authors: Lorenzo Facciaroni, Costantino Ricciuti, Enrico Scalas, Bruno Toaldo

Institutions: Sapienza University of Rome, University of Turin

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590