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Mathematics > Numerical Analysis

arXiv:2504.21523 (math)
[Submitted on 30 Apr 2025 (v1) , last revised 8 May 2025 (this version, v3)]

Title: Sibuya probability distributions and numerical evaluation of fractional-order operators

Title: Sibuya概率分布和分数阶算子的数值评估

Authors:Nikolai Leonenko, Igor Podlubny
Abstract: In this work we explore the Sibuya discrete probability distribution, which serves as the basis and the main instrument for numerical simulations of Grunwald--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, and suggest the notion of the continuous Sibuya probability distribution. 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.
Comments: 28 pages, 13 figures
Subjects: Numerical Analysis (math.NA) ; Probability (math.PR)
MSC classes: 65C05 (primary), 65D25, 26A33
Cite as: arXiv:2504.21523 [math.NA]
  (or arXiv:2504.21523v3 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2504.21523

Submission history

From: Igor Podlubny [view email]
[v1] Wed, 30 Apr 2025 11:18:39 UTC (1,247 KB)
[v2] Tue, 6 May 2025 15:36:43 UTC (1,247 KB)
[v3] Thu, 8 May 2025 12:57:54 UTC (1,117 KB)
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