Abelian groups of fractional operators

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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 2024-04-10T13:10:56Z
• dc.date.available 2024-04-10T13:10:56Z
• dc.date.issued 2022
• dc.description Comunicació presentada a la The 5th Mexican Workshop on Fractional Calculus, celebrada del 5 al 7 d'octubre de 2022 a Monterrey, Mèxic.
• dc.description.abstract Taking into count the large number of fractional operators that have been generated over the years, and considering that their number is unlikely to stop increasing at the time of writing this paper due to the recent boom of fractional calculus, everything seems to indicate that an alternative that allows to fully characterize some elements of fractional calculus is through the use of sets. Therefore, this paper presents a recapitulation of some fractional derivatives, fractional integrals, and local fractional operators that may be found in the literature, as well as a summary of how to define sets of fractional operators that allow to fully characterize some elements of fractional calculus, such as the Taylor series expansion of a scalar function in multi-index notation. In addition, it is presented a way to define finite and infinite Abelian groups of fractional operators through a family of sets of fractional operators and two different internal operations. Finally, using the above results, it is shown one way to define commutative and unitary rings of fractional operators.
• dc.format.mimetype application/pdf
• dc.identifier.citation Torres-Hernandez A, Brambila-Paz F, Ramirez-Melendez, R. Abelian groups of fractional operators. In: Cruz-Duarte JM; Toledo-Hernández P, editors. The 5th Mexican Workshop on Fractional Calculus (MWFC 2022). Computer Sciences & Mathematics Forum; 2022 Oct 5-7; Monterrey, Mexico. Basel: MDPI; 2022. 12 p. DOI: 10.3390/cmsf2022004004
• dc.identifier.doi http://dx.doi.org/10.3390/cmsf2022004004
• dc.identifier.issn 2813-0324
• dc.identifier.uri http://hdl.handle.net/10230/59725
• dc.language.iso eng
• dc.publisher MDPI
• dc.relation.ispartof Cruz-Duarte JM; Toledo-Hernández P, editors. The 5th Mexican Workshop on Fractional Calculus (MWFC 2022). Computer Sciences & Mathematics Forum; 2022 Oct 5-7; Monterrey, Mexico. Basel: MDPI; 2022. 12 p.
• dc.rights © 2022 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 (http://creativecommons.org/licenses/by/4.0/).
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0
• dc.subject.keyword fractional operators
• dc.subject.keyword set theory
• dc.subject.keyword group theory
• dc.subject.keyword fractional calculus of sets
• dc.title Abelian groups of fractional operators
• dc.type info:eu-repo/semantics/conferenceObject
• dc.type.version info:eu-repo/semantics/publishedVersion