Generalized fractional calculus and some models of generalized counting processes

Khrystyna Buchak; Lyudmyla Sakhno

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arXiv · 2312.04647

Generalized fractional calculus and some models of generalized counting processes

Khrystyna Buchak·Lyudmyla Sakhno

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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 Bern\v{s}tein functions. Some particular examples are presented.

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Khrystyna Buchak, Lyudmyla Sakhno. 2023-12-07. Generalized fractional calculus and some models of generalized counting processes. https://arxiv.org/abs/2312.04647

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