Publicação
Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case
| dc.contributor.author | Ferreira, Milton | |
| dc.contributor.author | Vieira, Nelson Felipe Loureiro | |
| dc.date.accessioned | 2019-02-07T16:00:47Z | |
| dc.date.available | 2019-02-07T16:00:47Z | |
| dc.date.issued | 2016-06 | |
| dc.description.abstract | In this paper, we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Ferreira M., and Vieira N., Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case, Complex Anal. Oper. Theory, 10(5), 2016, 1081-1100 | pt_PT |
| dc.identifier.doi | 10.1007/s11785-015-0529-9 | pt_PT |
| dc.identifier.issn | 1661-8254 | |
| dc.identifier.other | 1661-8262 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/3822 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer Nature [academic journals on nature.com] | pt_PT |
| dc.relation.publisherversion | https://link.springer.com/article/10.1007/s11785-015-0529-9 | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | Fractional partial differential equations | pt_PT |
| dc.subject | Fractional Laplace and Dirac operators | pt_PT |
| dc.subject | Riemann-Liouville derivatives and integrals of fractional order | pt_PT |
| dc.subject | Eigenfunctions and fundamental solution | pt_PT |
| dc.subject | Laplace transform | pt_PT |
| dc.subject | Mittag-Leffler function | pt_PT |
| dc.title | Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 1100 | pt_PT |
| oaire.citation.issue | 5 | pt_PT |
| oaire.citation.startPage | 1081 | pt_PT |
| oaire.citation.title | Complex Analysis and Operator Theory | pt_PT |
| oaire.citation.volume | 10 | pt_PT |
| person.familyName | Ferreira | |
| person.familyName | Vieira | |
| person.givenName | Milton | |
| person.givenName | Nelson | |
| person.identifier.ciencia-id | CA19-2009-F26D | |
| person.identifier.ciencia-id | 9418-DDFB-DE9D | |
| person.identifier.orcid | 0000-0003-1816-8293 | |
| 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 | 55576073000 | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
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