An introduction to weighted operators via composition and selected properties, aimed at numerical implementation

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dc.contributor.authorCamacho, Oscar
dc.contributor.authorChalco, Ronny
dc.contributor.authorDi Teodoro, Antonio
dc.contributor.authorGude, Juan José
dc.contributor.authorMontaluisa, Renato
dc.contributor.authorVargas, Carlos
dc.contributor.authorVega, Sebastián
dc.contributor.authorVillegas, María
dc.date.accessioned2026-04-22T13:22:55Z
dc.date.available2026-04-22T13:22:55Z
dc.date.issued2025-12
dc.date.updated2026-04-22T13:22:55Z
dc.descriptionPonencia presentada en la 3th IFAC Conference on Fractional Differentiation and its Applications ICFDA 2025, celebrada en Argelia entre el 16 y el 18 de diciembre de 2025es
dc.description.abstractThis work introduces a novel class of weighted fractional operators constructed through the composition of differential and integral operators. In particular, we propose the operator q¯Dxμ, which generalizes classical fractional derivatives while maintaining essential properties such as linearity. Although the semigroup property and the Leibniz rule do not hold in their traditional forms, we derive analogous formulations by combining the proposed operator with the Riemann-Liouville derivative. Furthermore, a numerical representation based on the Grünwald-Letnikov method is developed, enabling efficient discretization and simulation of the weighted operator in cases where analytical solutions are intractable. The approach also considers the interplay between Laplace transforms and convolutions, which is crucial for real-world applications in control and signal processing.en
dc.description.sponsorshipThis work was supported by the Basque Government (BEREZ-IA Elkartek Project, Grant KK-2023/00012) and by Universidad San Francisco de Quito (USFQ) through the Poli-Grants Program (Grant 33603)en
dc.identifier.citationCamacho, O., Chalco, R., Di Teodoro, A., Gude, J. J., Montaluisa, R., Vargas, C., Vega, S., & Villegas, M. (2025). An introduction to weighted operators via composition and selected properties, aimed at numerical implementation. IFAC-PapersOnLine, 59(37), 47-52. https://doi.org/10.1016/J.IFACOL.2026.01.009
dc.identifier.doi10.1016/J.IFACOL.2026.01.009
dc.identifier.eissn2405-8963
dc.identifier.issn2405-8971
dc.identifier.urihttps://hdl.handle.net/20.500.14454/5741
dc.language.isoeng
dc.publisherElsevier B.V.
dc.rightsCopyright © 2025 The Authors
dc.subject.otherComposition properties
dc.subject.otherFractional PID control
dc.subject.otherFractional systems
dc.subject.otherIndustrial Process Control
dc.subject.otherWeighted Operators
dc.titleAn introduction to weighted operators via composition and selected properties, aimed at numerical implementationen
dc.typeconference paper
dcterms.accessRightsopen access
oaire.citation.endPage52
oaire.citation.issue37
oaire.citation.startPage47
oaire.citation.titleIFAC-PapersOnLine
oaire.citation.volume59
oaire.licenseConditionhttps://creativecommons.org/licenses/by-nc-nd/4.0/
oaire.versionVoR
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