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A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

2015Journal article Restricted access
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dc.contributor.authorBhrawy, A. H.
dc.contributor.authorTaha, T. M.
dc.contributor.authorMachado, J.A.Tenreiro
dc.date.accessioned2015-11-20T11:54:37Z
dc.date.available2015-11-20T11:54:37Z
dc.date.issued2015
dc.description.abstractRecently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.pt_PT
dc.identifier.doi10.1007/s11071-015-2087-0pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.22/6963
dc.language.isoengpt_PT
dc.publisherSpringerpt_PT
dc.relation.ispartofseriesNonlinear Dynamics;Vol. 81, Issue 3
dc.relation.publisherversionhttp://link.springer.com/article/10.1007/s11071-015-2087-0pt_PT
dc.subjectMulti-term FDEspt_PT
dc.subjectOperational matricespt_PT
dc.subjectLegendre polynomialspt_PT
dc.subjectJacobi polynomialspt_PT
dc.subjectChebyshev polynomialspt_PT
dc.subjectBernstein polynomialspt_PT
dc.subjectGeneralized Laguerre polynomialspt_PT
dc.subjectModified generalized Laguerre polynomialspt_PT
dc.subjectTau methodpt_PT
dc.subjectCollocation methodpt_PT
dc.titleA Review of Operational Matrices and Spectral Techniques for Fractional Calculuspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage1052pt_PT
oaire.citation.startPage1023pt_PT
oaire.citation.titleNonlinear Dynamicspt_PT
oaire.citation.volume81pt_PT
person.familyNameTenreiro Machado
person.givenNameJ. A.
person.identifier.ciencia-id7A18-4935-5B29
person.identifier.orcid0000-0003-4274-4879
person.identifier.ridM-2173-2013
person.identifier.scopus-author-id55989030100
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication82cd5c17-07b6-492b-b3e3-ecebdad1254f
relation.isAuthorOfPublication.latestForDiscovery82cd5c17-07b6-492b-b3e3-ecebdad1254f

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