Proposal for use of the fractional derivative of radial functions in interpolation problems
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- dc.contributor.author Torres Hernandez, Anthony
- dc.contributor.author Brambila Paz, Fernando
- dc.contributor.author Ramírez, Rafael, 1966-
- dc.date.accessioned 2024-04-09T08:34:31Z
- dc.date.available 2024-04-09T08:34:31Z
- dc.date.issued 2024
- dc.description.abstract This paper presents the construction of a family of radial functions aimed at emulating the behavior of the radial basis function known as thin plate spline (TPS). Additionally, a method is proposed for applying fractional derivatives, both partially and fully, to these functions for use in interpolation problems. Furthermore, a technique is employed to precondition the matrices generated in the presented problems through 𝑄𝑅 decomposition. Similarly, a method is introduced to define two different types of abelian groups for any fractional operator defined in the interval [0,1) , among which the Riemann–Liouville fractional integral, Riemann–Liouville fractional derivative, and Caputo fractional derivative are worth mentioning. Finally, a form of radial interpolant is suggested for application in solving fractional differential equations using the asymmetric collocation method, and examples of its implementation in differential operators utilizing the aforementioned fractional operators are shown.
- dc.format.mimetype application/pdf
- dc.identifier.citation Torres-Hernandez A, Brambila-Paz F, Ramirez-Melendez R. Proposal for use of the fractional derivative of radial functions in interpolation problems. Fractal and fract. 2024;8(1):16. DOI: 10.3390/fractalfract8010016
- dc.identifier.doi http://dx.doi.org/10.3390/fractalfract8010016
- dc.identifier.issn 2504-3110
- dc.identifier.uri http://hdl.handle.net/10230/59698
- dc.language.iso eng
- dc.publisher MDPI
- dc.relation.ispartof Fractal and fractional. 2024;8(1):16.
- dc.rights © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri https://creativecommons.org/licenses/by/4.0/
- dc.subject.keyword radial basis functions
- dc.subject.keyword fractional operators
- dc.subject.keyword abelian groups
- dc.subject.keyword fractional calculus of sets
- dc.title Proposal for use of the fractional derivative of radial functions in interpolation problems
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion