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dc.contributor.authorAsl, Mohammad S.*
dc.contributor.authorJavidi, Mohammad*
dc.contributor.authorYan, Yubin*
dc.date.accessioned2018-01-24T11:37:07Z
dc.date.available2018-01-24T11:37:07Z
dc.date.issued2018-01-09
dc.identifier.citationAsl, M. S., Javidi, M., & Yan, Y. (2018). A novel high-order algorithm for the numerical estimation of fractional differential equations. Journal of Computational and Applied Mathematics, 342, 180-201. https://doi.org/10.1016/j.cam.2017.12.047en
dc.identifier.doi10.1016/j.cam.2017.12.047
dc.identifier.urihttp://hdl.handle.net/10034/620809
dc.description.abstractThis paper uses polynomial interpolation to design a novel high-order algorithm for the numerical estimation of fractional differential equations. The Riemann-Liouville fractional derivative is expressed by using the Hadamard finite-part integral and the piecewise cubic interpolation polynomial is utilized to approximate the integral. The detailed error analysis is presented and it is established that the convergence order of the algorithm is O(h4−a). Asymptotic expansion of the error for the presented algorithm is also investigated. Some numerical examples are provided and compared with the exact solution to show that the numerical results are in well agreement with the theoretical ones and also to illustrate the accuracy and efficiency of the proposed algorithm.
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0377042718300153?via%3Dihuben
dc.subjectFractional differential equationen
dc.subjectCaputo fractional derivativeen
dc.subjectRiemann-Liouville fractional derivativeen
dc.subjectError estimatesen
dc.subjectHadamard finite-part integralen
dc.titleA novel high-order algorithm for the numerical estimation of fractional differential equationsen
dc.typeArticleen
dc.identifier.eissn1879-1778
dc.contributor.departmentUniversity of Tabriz; University of Chesteren
dc.identifier.journalJournal of Computational and Applied Mathematics
dc.date.accepted2017-11-15
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2019-01-09
html.description.abstractThis paper uses polynomial interpolation to design a novel high-order algorithm for the numerical estimation of fractional differential equations. The Riemann-Liouville fractional derivative is expressed by using the Hadamard finite-part integral and the piecewise cubic interpolation polynomial is utilized to approximate the integral. The detailed error analysis is presented and it is established that the convergence order of the algorithm is O(h4−a). Asymptotic expansion of the error for the presented algorithm is also investigated. Some numerical examples are provided and compared with the exact solution to show that the numerical results are in well agreement with the theoretical ones and also to illustrate the accuracy and efficiency of the proposed algorithm.
rioxxterms.publicationdate2018-01-09


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