Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes

Gupta, Neha, Kumar, Arun, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Vaz, Jayme 2024. Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes. Fractional Calculus and Applied Analysis 27 , pp. 1527-1563. 10.1007/s13540-024-00289-x

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Abstract

In this article, convolution-type fractional derivatives generated by Dickman subordinator and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse are generalizations of stable and inverse stable subordinators, respectively. The series representations of densities of the Dickman subordinator and inverse Dickman subordinator are also obtained, which could be helpful for computational purposes. Moreover, the space and time-fractional Poisson-Dickman processes, space-fractional Skellam Dickman process and non-homogenous Poisson-Dickman process are introduced and their main properties are studied.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag
Date of First Compliant Deposit:	26 April 2024
Date of Acceptance:	24 April 2024
Last Modified:	31 Jul 2024 13:42
URI:	https://orca.cardiff.ac.uk/id/eprint/168428

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