Please use this identifier to cite or link to this item: `http://hdl.handle.net/10773/32652`
DC FieldValueLanguage
dc.contributor.authorNemati, Somayehpt_PT
dc.contributor.authorLima, Pedro M.pt_PT
dc.contributor.authorTorres, Delfim F. M.pt_PT
dc.date.accessioned2021-11-24T12:01:31Z-
dc.date.available2021-11-24T12:01:31Z-
dc.date.issued2021-11-14-
dc.identifier.urihttp://hdl.handle.net/10773/32652-
dc.description.abstractWe introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the Riemann–Liouville integral operator was used to give approximations for the unknown function and its variable-order derivatives. An operational matrix of variable-order fractional integration was introduced for the Bernoulli functions. By assuming that the solution of the problem is sufficiently smooth, we approximated a given order of its derivative using Bernoulli polynomials. Then, we used the introduced operational matrix to find some approximations for the unknown function and its derivatives. Using these approximations and some collocation points, the problem was reduced to the solution of a system of nonlinear algebraic equations. An error estimate is given for the approximate solution obtained by the proposed method. Finally, five illustrative examples were considered to demonstrate the applicability and high accuracy of the proposed technique, comparing our results with the ones obtained by existing methods in the literature and making clear the novelty of the work. The numerical results showed that the new method is efficient, giving high-accuracy approximate solutions even with a small number of basis functions and when the solution to the problem is not infinitely differentiable, providing better results and a smaller number of basis functions when compared to state-of-the-art methods.pt_PT
dc.language.isoengpt_PT
dc.publisherMDPIpt_PT
dc.relationUIDB/04621/2020pt_PT
dc.relationUIDB/04106/2020pt_PT
dc.rightsopenAccesspt_PT
dc.subjectFractional differential equationspt_PT
dc.subjectNumerical methodspt_PT
dc.subjectVariable-order fractional calculuspt_PT
dc.subjectOperational matrix of variable-order fractional integrationpt_PT
dc.subjectBernoulli polynomialspt_PT
dc.titleNumerical solution of variable-order fractional differential equations using Bernoulli polynomialspt_PT
dc.typearticlept_PT
dc.description.versionpublishedpt_PT
dc.peerreviewedyespt_PT
degois.publication.issue4pt_PT
degois.publication.titleFractal and Fractionalpt_PT
degois.publication.volume5pt_PT
dc.relation.publisherversionhttps://www.mdpi.com/2504-3110/5/4/219pt_PT
dc.identifier.doi10.3390/fractalfract5040219pt_PT
dc.identifier.essn2504-3110pt_PT
dc.identifier.articlenumber219pt_PT
Appears in Collections:CIDMA - Artigos
DMat - Artigos
SCG - Artigos

Files in This Item:
File Description SizeFormat