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A Simple Solution for the General Fractional Ambartsumian Equation

2023-01-08Artigo científico Acesso aberto
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dc.contributor.authorOrtigueira, Manuel Duarte
dc.contributor.authorBengochea, Gabriel
dc.contributor.institutionCTS - Centro de Tecnologia e Sistemas
dc.contributor.institutionDEE - Departamento de Engenharia Electrotécnica e de Computadores
dc.contributor.institutionUNINOVA-Instituto de Desenvolvimento de Novas Tecnologias
dc.contributor.pblMDPI - Multidisciplinary Digital Publishing Institute
dc.date.accessioned2023-07-11T22:22:25Z
dc.date.available2023-07-11T22:22:25Z
dc.date.issued2023-01-08
dc.descriptionFunding Information: The second author was supported by the Autonomous University of Mexico City (UACM) under the project Ccyt-2021-11. Publisher Copyright: © 2023 by the authors.
dc.description.abstractFractionalisation and solution of the Ambartsumian equation is considered. The general approach to fractional calculus suitable for applications in physics and engineering is described. It is shown that Liouville-type derivatives are the necessary ones, because they fully preserve backward compatibility with classical results. Such derivatives are used to define and solve the fractional Ambartsumian equation. First, a solution in terms of a slowly convergent fractional Taylor series is obtained. Then, a simple solution expressed in terms of an infinite linear combination of Mittag–Leffler functions is deduced. A fast algorithm, based on a bilinear transformation and using the fast Fourier transform, is described and demonstrated for its approximate numerical realisation.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent15
dc.format.extent434671
dc.identifier.doi10.3390/app13020871
dc.identifier.issn2076-3417
dc.identifier.otherPURE: 65875499
dc.identifier.otherPURE UUID: a1225a6c-f0ad-41ba-8f67-c4f385a9b4f4
dc.identifier.otherScopus: 85146730967
dc.identifier.otherWOS: 000916931200001
dc.identifier.otherORCID: /0000-0003-4270-3284/work/151429123
dc.identifier.urihttp://hdl.handle.net/10362/155105
dc.identifier.urlhttps://www.scopus.com/pages/publications/85146730967
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT
dc.relationCentre of Technology and Systems
dc.subjectAmbartsumian equation
dc.subjectbilinear transformation
dc.subjectfractional derivative
dc.subjectGrünwald–Letnikov
dc.subjectMittag–Leffler function
dc.subjectGeneral Materials Science
dc.subjectInstrumentation
dc.subjectGeneral Engineering
dc.subjectProcess Chemistry and Technology
dc.subjectComputer Science Applications
dc.subjectFluid Flow and Transfer Processes
dc.titleA Simple Solution for the General Fractional Ambartsumian Equationen
dc.typejournal article
degois.publication.issue2
degois.publication.titleApplied Sciences
degois.publication.volume13
dspace.entity.typePublication
oaire.awardNumberUIDB/00066/2020
oaire.awardTitleCentre of Technology and Systems
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublication779ae807-14a4-4e58-87e2-6dd81eb7a030
relation.isProjectOfPublication.latestForDiscovery779ae807-14a4-4e58-87e2-6dd81eb7a030

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