Torres Hernandez, AnthonyBrambila Paz, FernandoIturrarán Viveros, UrsulaCaballero Cruz, Reyna2024-04-302024-04-302021Torres-Hernandez A, Brambila-Paz F, Iturrarán-Viveros U, Caballero-Cruz R. Fractional Newton–Raphson method accelerated with aitken’s method. Anxioms. 2021;10(2):47. DOI: 10.3390/axioms100200472075-1680http://hdl.handle.net/10230/59955In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton–Raphson (F N–R) method, which seems to have an order of convergence at least linearly for the case in which the order 𝛼 of the derivative is different from one. A simplified way of constructing the Riemann–Liouville (R–L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken’s method is made and it is explained why it has the ability to accelerate the convergence of the iterative methods, in order to finally present the results that were obtained when implementing Aitken’s method in the F N–R method, where it is shown that F N–R with Aitken’s method converges faster than the simple F N–R.application/pdfeng© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/4.0/).Fractional Newton–Raphson method accelerated with aitken’s methodinfo:eu-repo/semantics/articlehttp://dx.doi.org/10.3390/axioms10020047Newton–Raphson methodfractional calculusfractional derivativeAitken’s methodinfo:eu-repo/semantics/openAccess