Sibuya probability distribution and numerical evaluation of fractional-order operators

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Podlubny, Igor 2026. Sibuya probability distribution and numerical evaluation of fractional-order operators. Fractional Calculus and Applied Analysis: An International Journal for Theory and Applications 10.1007/s13540-026-00547-0

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Abstract

In this work we explore the Sibuya probability distribution, which serves as the basis and the main instrument for numerical simulations of Grünwald–Letnikov fractional derivatives by the Monte Carlo method. We provide three methods for simulating the Sibuya distribution. We also introduce the Sibuya-like sieved probability distributions, and apply them to numerical fractional-order differentiation. Additionally, we use the Monte Carlo method for evaluating fractional-order integrals. The developed methods and tools are illustrated by examples of computation. We provide the MATLAB toolboxes for simulation of the Sibuya probability distribution, and for the numerical examples.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Springer
ISSN:	1311-0454
Funders:	EPSRC
Projects:	EP/R014604/1, EP/Z000580/1
Date of First Compliant Deposit:	2 June 2026
Date of Acceptance:	29 May 2026
Last Modified:	20 Aug 2026 15:08
URI:	https://orca.cardiff.ac.uk/id/eprint/187374

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