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A Variant of Chebyshev's Method with 3 alpha th-Order of Convergence by Using Fractional Derivatives

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A Variant of Chebyshev's Method with 3 alpha th-Order of Convergence by Using Fractional Derivatives

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Girona, Ivan es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2020-05-22T03:02:55Z
dc.date.available 2020-05-22T03:02:55Z
dc.date.issued 2019-08-06 es_ES
dc.identifier.uri http://hdl.handle.net/10251/144099
dc.description.abstract [EN] In this manuscript, we propose several iterative methods for solving nonlinear equations whose common origin is the classical Chebyshev's method, using fractional derivatives in their iterative expressions. Due to the symmetric duality of left and right derivatives, we work with right-hand side Caputo and Riemann-Liouville fractional derivatives. To increase as much as possible the order of convergence of the iterative scheme, some improvements are made, resulting in one of them being of 3 alpha-th order. Some numerical examples are provided, along with an study of the dependence on initial estimations on several test problems. This results in a robust performance for values of alpha close to one and almost any initial estimation. es_ES
dc.description.sponsorship This research was partially supported by Ministerio de Ciencia, Innovacion y Universidades under grants PGC2018-095896-B-C22 and by Generalitat Valenciana PROMETEO/2016/089. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Symmetry (Basel) es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Nonlinear equations es_ES
dc.subject Chebyshev s iterative method es_ES
dc.subject Fractional derivative es_ES
dc.subject Basin of attraction es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A Variant of Chebyshev's Method with 3 alpha th-Order of Convergence by Using Fractional Derivatives es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/sym11081017 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2016%2F089/ES/Resolución de ecuaciones y sistemas no lineales mediante técnicas iterativas: análisis dinámico y aplicaciones/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095896-B-C22/ES/DISEÑO, ANALISIS Y ESTABILIDAD DE PROCESOS ITERATIVOS APLICADOS A LAS ECUACIONES INTEGRALES Y MATRICIALES Y A LA COMUNICACION AEROESPACIAL/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Cordero Barbero, A.; Girona, I.; Torregrosa Sánchez, JR. (2019). A Variant of Chebyshev's Method with 3 alpha th-Order of Convergence by Using Fractional Derivatives. Symmetry (Basel). 11(8):1-11. https://doi.org/10.3390/sym11081017 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/sym11081017 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 11 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 11 es_ES
dc.description.issue 8 es_ES
dc.identifier.eissn 2073-8994 es_ES
dc.relation.pasarela S\393520 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.description.references Altaf Khan, M., Ullah, S., & Farhan, M. (2019). The dynamics of Zika virus with Caputo fractional derivative. AIMS Mathematics, 4(1), 134-146. doi:10.3934/math.2019.1.134 es_ES
dc.description.references Akgül, A., Cordero, A., & Torregrosa, J. R. (2019). A fractional Newton method with 2αth-order of convergence and its stability. Applied Mathematics Letters, 98, 344-351. doi:10.1016/j.aml.2019.06.028 es_ES
dc.description.references Caputo, M. C., & Torres, D. F. M. (2015). Duality for the left and right fractional derivatives. Signal Processing, 107, 265-271. doi:10.1016/j.sigpro.2014.09.026 es_ES
dc.description.references Odibat, Z. M., & Shawagfeh, N. T. (2007). Generalized Taylor’s formula. Applied Mathematics and Computation, 186(1), 286-293. doi:10.1016/j.amc.2006.07.102 es_ES
dc.description.references Magreñán, Á. A. (2014). A new tool to study real dynamics: The convergence plane. Applied Mathematics and Computation, 248, 215-224. doi:10.1016/j.amc.2014.09.061 es_ES


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