dc.contributor.author Asl, Mohammad S. * dc.contributor.author Javidi, Mohammad * dc.contributor.author Yan, Yubin * dc.date.accessioned 2018-01-24T11:37:07Z dc.date.available 2018-01-24T11:37:07Z dc.date.issued 2018-01-09 dc.identifier.citation Asl, 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.2017.12.047 en dc.identifier.doi 10.1016/j.cam.2017.12.047 dc.identifier.uri http://hdl.handle.net/10034/620809 dc.description.abstract This 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.iso en en dc.publisher Elsevier en dc.relation.url http://www.sciencedirect.com/science/article/pii/S0377042718300153?via%3Dihub en dc.subject Fractional differential equation en dc.subject Caputo fractional derivative en dc.subject Riemann-Liouville fractional derivative en dc.subject Error estimates en dc.subject Hadamard finite-part integral en dc.title A novel high-order algorithm for the numerical estimation of fractional differential equations en dc.type Article en dc.identifier.eissn 1879-1778 dc.contributor.department University of Tabriz; University of Chester en dc.identifier.journal Journal of Computational and Applied Mathematics dc.date.accepted 2017-11-15 or.grant.openaccess Yes en rioxxterms.funder Unfunded en rioxxterms.identifier.project Unfunded en rioxxterms.version AM en rioxxterms.licenseref.startdate 2019-01-09 html.description.abstract This 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.publicationdate 2018-01-09
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