Generalized fractional calculus and some models of generalized counting processes

2023/12/07 by Khrystyna Buchak, Buchak, Khrystyna, Lyudmyla Sakhno +1 · 1 citation
Mathematics · Physics and Astronomy · #60G50 #60G51 #60G55 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Dynamics and Fractals #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2312.04647

openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the generalized fractional derivatives, namely, convolutions-type derivatives with respect to Bernštein functions. Some particular examples are presented.

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