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Peer-reviewedCC BY 4.0Fractional Calculus & Applied Analysis

Sibuya probability distribution and numerical evaluation of fractional-order operators

  • Nikolai Leonenko1
  • Igor Podlubny2
  1. 1School of Mathematics, Cardiff University, Cardiff, CF 24 4AG United Kingdom
  2. 2BERG Faculty, Technical University of Kosice, Nemcovej 3, 04200 Kosice, Slovakia
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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.

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Cite

BibTeXRIS
BibTeX
@article{leonenko2026sibuya,
  title = {{Sibuya probability distribution and numerical evaluation of fractional-order operators}},
  author = {Nikolai Leonenko and Igor Podlubny},
  journal = {Fractional Calculus \& Applied Analysis},
  year = {2026},
  month = jun,
  doi = {10.1007/s13540-026-00547-0},
  url = {https://doi.org/10.1007/s13540-026-00547-0},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Sibuya probability distribution and numerical evaluation of fractional-order operators
AU  - Nikolai Leonenko
AU  - Igor Podlubny
PY  - 2026
DA  - 2026/06/29
JO  - Fractional Calculus & Applied Analysis
DO  - 10.1007/s13540-026-00547-0
UR  - https://doi.org/10.1007/s13540-026-00547-0
AB  - 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.
SN  - 1311-0454
SN  - 1314-2224
ER  -