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Multipoint Fractional Iterative Methods with (2 α + 1)th-Order of Convergence for Solving Nonlinear Problems

Author

Listed:
  • Giro Candelario

    (Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Santo Domingo 10602, Dominican Republic)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain)

Abstract

In the recent literature, some fractional one-point Newton-type methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper, we introduce a new fractional Newton-type method with order of convergence α + 1 and compare it with the existing fractional Newton method with order 2 α . Moreover, we also introduce a multipoint fractional Traub-type method with order 2 α + 1 and compare its performance with that of its first step. Some numerical tests and analysis of the dependence on the initial estimations are made for each case, including a comparison with classical Newton ( α = 1 of the first step of the class) and classical Traub’s scheme ( α = 1 of fractional proposed multipoint method). In this comparison, some cases are found where classical Newton and Traub’s methods do not converge and the proposed methods do, among other advantages.

Suggested Citation

  • Giro Candelario & Alicia Cordero & Juan R. Torregrosa, 2020. "Multipoint Fractional Iterative Methods with (2 α + 1)th-Order of Convergence for Solving Nonlinear Problems," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:452-:d:335114
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    References listed on IDEAS

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    1. A.M. Mathai & H.J. Haubold, 2017. "Fractional and Multivariable Calculus," Springer Optimization and Its Applications, Springer, number 978-3-319-59993-9, September.
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    Cited by:

    1. Torres-Hernandez, A. & Brambila-Paz, F. & Montufar-Chaveznava, R., 2022. "Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers," Applied Mathematics and Computation, Elsevier, vol. 429(C).

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