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dc.contributor.authorGrigoletto, Eliana Contharteze [UNESP]
dc.contributor.authorde Oliveira, Edmundo Capelas
dc.contributor.authorde Figueiredo Camargo, Rubens [UNESP]
dc.date.accessioned2018-12-11T16:53:26Z
dc.date.available2018-12-11T16:53:26Z
dc.date.issued2018-05-01
dc.identifierhttp://dx.doi.org/10.1007/s40314-016-0381-1
dc.identifier.citationComputational and Applied Mathematics, v. 37, n. 2, p. 1012-1026, 2018.
dc.identifier.issn1807-0302
dc.identifier.issn0101-8205
dc.identifier.urihttp://hdl.handle.net/11449/171031
dc.description.abstractEigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann–Liouville fractional derivative. A second application consists of an initial value problem for a fractional wave equation in two dimensions in which the integer order partial derivative with respect to the time variable is replaced by the Caputo fractional derivative. The classical Mittag-Leffler functions are important in the theory of fractional calculus because they emerge as solutions of fractional differential equations. Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. A remarkable characteristic of this relation is that it is true for any value of the parameter n appearing in the definition of the functions, i.e., we have an infinite family of different expressions for ex in terms of classical Mittag-Leffler functions.en
dc.format.extent1012-1026
dc.language.isoeng
dc.relation.ispartofComputational and Applied Mathematics
dc.sourceScopus
dc.subjectCaputo derivatives
dc.subjectLinear fractional differential equations
dc.subjectMittag-Leffler functions
dc.subjectRiemann–Liouville derivatives
dc.titleLinear fractional differential equations and eigenfunctions of fractional differential operatorsen
dc.typeArtigo
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.description.affiliationDepartamento de Bioprocessos e Biotecnologia FCA-UNESP, Rua José Barbosa de Barros 1780
dc.description.affiliationDepartamento de Matemática Aplicada IMECC-UNICAMP
dc.description.affiliationDepartamento de Matemática Faculdade de Ciências UNESP, Av. Eng. Luiz Edmundo Carrijo Coube, 14-01 Bairro: Vargem Limpa
dc.description.affiliationUnespDepartamento de Bioprocessos e Biotecnologia FCA-UNESP, Rua José Barbosa de Barros 1780
dc.description.affiliationUnespDepartamento de Matemática Faculdade de Ciências UNESP, Av. Eng. Luiz Edmundo Carrijo Coube, 14-01 Bairro: Vargem Limpa
dc.identifier.doi10.1007/s40314-016-0381-1
dc.rights.accessRightsAcesso aberto
dc.identifier.scopus2-s2.0-85047440508
dc.identifier.file2-s2.0-85047440508.pdf
dc.identifier.lattes6909447212349406
dc.identifier.orcid0000-0003-4336-5387
unesp.author.lattes6909447212349406[1]
unesp.author.orcid0000-0003-4336-5387[1]
unesp.author.orcid0000-0003-4336-5387[1]
dc.relation.ispartofsjr0,272
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