Fractional Newton-Raphson method and some variants for the solution of nonlinear systems
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- dc.contributor.author Torres Hernandez, Anthony
- dc.contributor.author Brambila Paz, Fernando
- dc.contributor.author De-la-Vega, Eduardo
- dc.date.accessioned 2025-07-03T06:40:25Z
- dc.date.available 2025-07-03T06:40:25Z
- dc.date.issued 2020
- dc.description.abstract The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow us to find solutions for some nonlinear systems in the complex space using real initial conditions. The origin of these methods is the fractional Newton-Raphson method, but unlike the latter, the orders proposed here for the fractional derivatives are functions. In the first method, a function is used to guarantee an order of convergence (at least) quadratic, and in the other, a function is used to avoid the discontinuity that is generated when the fractional derivative of the constants is used, and with this, it is possible that the method has at most an order of convergence (at least) linear
- dc.format.mimetype application/pdf
- dc.identifier.citation Torres-Hernandez A, Brambila-Paz F, De-la-Vega E. Fractional Newton-Raphson method and some variants for the solution of nonlinear systems. MathSJ. 2020 Mar;7(1):13-27. DOI: 10.5121/mathsj.2020.7102
- dc.identifier.doi http://dx.doi.org/10.5121/mathsj.2020.7102
- dc.identifier.issn 2349-6223
- dc.identifier.uri http://hdl.handle.net/10230/70823
- dc.language.iso eng
- dc.publisher AIRCC Publishing Corporation
- dc.relation.ispartof Applied Mathematics and Sciences: an International Journal. 2020 Mar;7(1):13-27
- dc.rights This article is distributed under the terms of the Creative Commons Attribution License (CC BY 4.0).
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by/4.0/
- dc.subject.keyword Iteration function
- dc.subject.keyword Order of convergence
- dc.subject.keyword Fractional derivative
- dc.title Fractional Newton-Raphson method and some variants for the solution of nonlinear systems
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion