dc.contributor.author Grigoletto, Eliana Contharteze [UNESP] dc.contributor.author de Oliveira, Edmundo Capelas dc.contributor.author de Figueiredo Camargo, Rubens [UNESP] dc.date.accessioned 2018-12-11T16:53:26Z dc.date.available 2018-12-11T16:53:26Z dc.date.issued 2018-05-01 dc.identifier http://dx.doi.org/10.1007/s40314-016-0381-1 dc.identifier.citation Computational and Applied Mathematics, v. 37, n. 2, p. 1012-1026, 2018. dc.identifier.issn 1807-0302 dc.identifier.issn 0101-8205 dc.identifier.uri http://hdl.handle.net/11449/171031 dc.description.abstract Eigenfunctions 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.extent 1012-1026 dc.language.iso eng dc.relation.ispartof Computational and Applied Mathematics dc.source Scopus dc.subject Caputo derivatives dc.subject Linear fractional differential equations dc.subject Mittag-Leffler functions dc.subject Riemann–Liouville derivatives dc.title Linear fractional differential equations and eigenfunctions of fractional differential operators en dc.type Artigo dc.contributor.institution Universidade Estadual Paulista (Unesp) dc.contributor.institution Universidade Estadual de Campinas (UNICAMP) dc.description.affiliation Departamento de Bioprocessos e Biotecnologia FCA-UNESP, Rua José Barbosa de Barros 1780 dc.description.affiliation Departamento de Matemática Aplicada IMECC-UNICAMP dc.description.affiliation Departamento de Matemática Faculdade de Ciências UNESP, Av. Eng. Luiz Edmundo Carrijo Coube, 14-01 Bairro: Vargem Limpa dc.description.affiliationUnesp Departamento de Bioprocessos e Biotecnologia FCA-UNESP, Rua José Barbosa de Barros 1780 dc.description.affiliationUnesp Departamento de Matemática Faculdade de Ciências UNESP, Av. Eng. Luiz Edmundo Carrijo Coube, 14-01 Bairro: Vargem Limpa dc.identifier.doi 10.1007/s40314-016-0381-1 dc.rights.accessRights Acesso aberto dc.identifier.scopus 2-s2.0-85047440508 dc.identifier.file 2-s2.0-85047440508.pdf dc.identifier.lattes 6909447212349406 dc.identifier.orcid 0000-0003-4336-5387 unesp.author.lattes 6909447212349406[1] unesp.author.orcid 0000-0003-4336-5387[1] unesp.author.orcid 0000-0003-4336-5387[1] dc.relation.ispartofsjr 0,272