Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation

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

Publication

Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation

2021-06-10Journal article

dc.contributor.author	Ferreira, M.
dc.contributor.author	Rodrigues, M. Manuela
dc.contributor.author	Vieira, Nelson
dc.date.accessioned	2022-08-05T13:47:10Z
dc.date.available	2022-08-05T13:47:10Z
dc.date.issued	2021-06-10
dc.description.abstract	In this paper, we consider a non-homogeneous time-space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm-Liouville operator defined in terms of right and left fractional Riemann-Liouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and non-homogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate Mittag-Leffler function. In the end of the paper, some illustrative examples are presented.	pt_PT
dc.description.version	info:eu-repo/semantics/publishedVersion	pt_PT
dc.identifier.citation	Ferreira, M., Rodrigues, M.M., and Vieira, N., Application of the Fractional Sturm-Liouville Theory to a Fractional Sturm-Liouville Telegraph Equation. Complex Analysis and Operator Theory 15(5), Article ID: 87, 2021	pt_PT
dc.identifier.doi	10.1007/s11785-021-01125-3	pt_PT
dc.identifier.uri	http://hdl.handle.net/10400.8/7511
dc.language.iso	eng	pt_PT
dc.peerreviewed	yes	pt_PT
dc.publisher	Springer	pt_PT
dc.relation	Center for Research and Development in Mathematics and Applications
dc.relation.ispartofseries	87;
dc.relation.publisherversion	https://link.springer.com/article/10.1007/s11785-021-01125-3	pt_PT
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	pt_PT
dc.subject	Caputo fractional derivatives	pt_PT
dc.subject	Riemann-Liouville fractional derivatives	pt_PT
dc.subject	Fractional Sturm-Liouville operator	pt_PT
dc.subject	Time-space-fractional telegraph equation	pt_PT
dc.subject	Mittag-Leffler functions	pt_PT
dc.subject	Wright functions	pt_PT
dc.title	Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation	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	36	pt_PT
oaire.citation.issue	5	pt_PT
oaire.citation.startPage	1	pt_PT
oaire.citation.title	Complex Analysis and Operator Theory	pt_PT
oaire.citation.volume	15	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
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person.identifier.scopus-author-id	22835991500
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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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