Monte Carlo method for fractional order differentiation

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Podlubny, Igor 2022. Monte Carlo method for fractional order differentiation. Fractional Calculus and Applied Analysis 25 , pp. 346-361. 10.1007/s13540-022-00017-3

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Abstract

In this work the Monte Carlo method is introduced for numerical evaluation of fractional-order derivatives. A general framework for using this method is presented and illustrated by several examples. The proposed method can be used for numerical evaluation of the Grünwald-Letnikov fractional derivatives, the Riemann-Liouville fractional derivatives, and also of the Caputo fractional derivatives, when they are equivalent to the Riemann-Liouville derivatives. The proposed method can be enhanced using standard approaches for the classic Monte Carlo method, and it also allows easy parallelization, which means that it is of high potential for applications of the fractional calculus.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Additional Information:	This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher:	Springer Science and Business Media
ISSN:	1311-0454
Date of First Compliant Deposit:	20 April 2022
Date of Acceptance:	20 March 2022
Last Modified:	03 Jun 2023 01:08
URI:	https://orca.cardiff.ac.uk/id/eprint/149223

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