A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem

Ferreira, Milton; Rodrigues, M. Manuela; Vieira, Nelson

Publication

A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem

2021Journal article

dc.contributor.author	Ferreira, Milton
dc.contributor.author	Rodrigues, M. Manuela
dc.contributor.author	Vieira, Nelson
dc.date.accessioned	2022-08-05T13:19:57Z
dc.date.available	2022-08-05T13:19:57Z
dc.date.issued	2021
dc.description.abstract	In this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.	pt_PT
dc.description.version	info:eu-repo/semantics/publishedVersion	pt_PT
dc.identifier.citation	Ferreira, M., Manuela Rodrigues, M. & Vieira, N. (2021). A fractional analysis in higher dimensions for the Sturm-Liouville problem. Fractional Calculus and Applied Analysis, 24(2), 585-620. https://doi.org/10.1515/fca-2021-0026	pt_PT
dc.identifier.doi	10.1515/fca-2021-0026	pt_PT
dc.identifier.uri	http://hdl.handle.net/10400.8/7510
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.publisher	De Gruyter	pt_PT
dc.relation	Center for Research and Development in Mathematics and Applications
dc.relation.ispartofseries	2;
dc.relation.publisherversion	https://www.degruyter.com/document/doi/10.1515/fca-2021-0026/html	pt_PT
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	pt_PT
dc.subject	Fractional derivatives	pt_PT
dc.subject	Fractional Sturm-Liouville problem	pt_PT
dc.subject	Fractional variational calculus	pt_PT
dc.subject	Eigenvalue problem	pt_PT
dc.subject	Eigenfunctions	pt_PT
dc.subject	Fractional Clifford analysis	pt_PT
dc.title	A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem	pt_PT
dc.type	journal article
dspace.entity.type	Publication
oaire.awardTitle	Center for Research and Development in Mathematics and Applications
oaire.awardURI	info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04106%2F2020/PT
oaire.citation.endPage	620	pt_PT
oaire.citation.startPage	585	pt_PT
oaire.citation.title	Fractional Calculus and Applied Analysis	pt_PT
oaire.citation.volume	24	pt_PT
oaire.fundingStream	6817 - DCRRNI ID
person.familyName	Ferreira
person.familyName	Rodrigues
person.familyName	Vieira
person.givenName	Milton
person.givenName	M. Manuela
person.givenName	Nelson
person.identifier.ciencia-id	CA19-2009-F26D
person.identifier.ciencia-id	461D-A5E2-23BE
person.identifier.ciencia-id	9418-DDFB-DE9D
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person.identifier.orcid	0000-0002-8834-5841
person.identifier.orcid	0000-0001-8756-4893
person.identifier.rid	A-2004-2015
person.identifier.rid	H-9130-2013
person.identifier.scopus-author-id	12144179800
person.identifier.scopus-author-id	22835991500
person.identifier.scopus-author-id	55576073000
project.funder.identifier	http://doi.org/10.13039/501100001871
project.funder.name	Fundação para a Ciência e a Tecnologia
rcaap.rights	openAccess	pt_PT
rcaap.type	article	pt_PT
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