Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/342812
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dc.contributor.CRUESPUNIVERSIDADE ESTADUAL DE CAMPINASpt_BR
dc.contributor.authorunicampSousa, José Vanterler da Costa-
dc.contributor.authorunicampOliveira, Edmundo Capelas de-
dc.typeArtigopt_BR
dc.titleOn the local M-derivativept_BR
dc.contributor.authorSousa, J. V. C.-
dc.contributor.authorde Oliveira, E. C.-
dc.subjectEquações diferenciais linearespt_BR
dc.subject.otherlanguageLinear differential equationspt_BR
dc.description.abstractWe denote a new differential operator by DM α,β(·), where the parameter a, associated with the order, is such that 0 < α < 1, β > 0 and M is used to denote that the function to be derived involves a Mittag-Leffler function with one parameter. This new derivative satisfies some properties of integer-order calculus, e.g. linearity, product rule, quotient rule, function composition and the chain rule. Besides as in the case of the Caputo derivative, the derivative of a constant is zero. Because Mittag-Leffler function is a natural generalization of the exponential function, we can extend some of the classical results, namely: Rolle's theorem, the mean-value theorem and its extension. We present the corresponding M-integral from which, as a natural consequence, new results emerge which can be interpreted as applications. Specifically, we generalize the inversion property of the fundamental theorem of calculus and prove a theorem associated with the classical integration by parts. Finally, we present an application involving linear differential equations by means of local M-derivative with some graphspt_BR
dc.relation.ispartofProgress in Fractional Differentiation and Applicationspt_BR
dc.relation.ispartofabbreviationProgr. fract. differ. appl.pt_BR
dc.publisher.cityNew York, NYpt_BR
dc.publisher.countryEstados Unidospt_BR
dc.publisherNatural Sciences Publishingpt_BR
dc.date.issued2018-
dc.language.isoengpt_BR
dc.description.volume4pt_BR
dc.description.issuenumber4pt_BR
dc.description.firstpage479pt_BR
dc.description.lastpage492pt_BR
dc.rightsAbertopt_BR
dc.sourceSCOPUSpt_BR
dc.identifier.issn2356-9336pt_BR
dc.identifier.eissn2356-9344pt_BR
dc.identifier.doi10.18576/pfda/040403pt_BR
dc.identifier.urlhttp://www.naturalspublishing.com/ContIss.asp?IssID=545pt_BR
dc.date.available2020-06-05T19:05:54Z-
dc.date.accessioned2020-06-05T19:05:54Z-
dc.description.provenanceSubmitted by Sanches Olivia (olivias@unicamp.br) on 2020-06-05T19:05:54Z No. of bitstreams: 0. Added 1 bitstream(s) on 2020-09-03T11:55:53Z : No. of bitstreams: 1 2-s2.0-85054424493.pdf: 240411 bytes, checksum: cf6d166742608917adce62a478bd3420 (MD5)en
dc.description.provenanceMade available in DSpace on 2020-06-05T19:05:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2019en
dc.identifier.urihttp://repositorio.unicamp.br/jspui/handle/REPOSIP/342812-
dc.contributor.departmentsem informaçãopt_BR
dc.contributor.departmentDepartamento de Matemáticapt_BR
dc.contributor.unidadeInstituto de Matemática, Estatística e Computação Científicapt_BR
dc.contributor.unidadeInstituto de Matemática, Estatística e Computação Científicapt_BR
dc.subject.keywordLocal M-derivativept_BR
dc.subject.keywordLocal M-differential equationpt_BR
dc.subject.keywordM-integralpt_BR
dc.subject.keywordMittag-Leffler functionpt_BR
dc.identifier.source2-s2.0-85054424493pt_BR
dc.creator.orcid0000-0002-6986-948Xpt_BR
dc.creator.orcid0000-0001-9661-0281pt_BR
dc.type.formArtigopt_BR
dc.description.otherSponsorshipsem informaçãopt_BR
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