{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T14:09:37Z","timestamp":1762956577411,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T00:00:00Z","timestamp":1617148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the following paper, we present a way to accelerate the speed of convergence of the fractional Newton\u2013Raphson (F N\u2013R) method, which seems to have an order of convergence at least linearly for the case in which the order \u03b1 of the derivative is different from one. A simplified way of constructing the Riemann\u2013Liouville (R\u2013L) fractional operators, fractional integral and fractional derivative is presented along with examples of its application on different functions. Furthermore, an introduction to Aitken\u2019s 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\u2019s method in the F N\u2013R method, where it is shown that F N\u2013R with Aitken\u2019s method converges faster than the simple F N\u2013R.<\/jats:p>","DOI":"10.3390\/axioms10020047","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T10:24:33Z","timestamp":1617186273000},"page":"47","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Fractional Newton\u2013Raphson Method Accelerated with Aitken\u2019s Method"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6496-9505","authenticated-orcid":false,"given":"A.","family":"Torres-Hernandez","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Science, UNAM, Mexico City 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7896-6460","authenticated-orcid":false,"given":"F.","family":"Brambila-Paz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, UNAM, Mexico City 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6410-7542","authenticated-orcid":false,"given":"U.","family":"Iturrar\u00e1n-Viveros","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, UNAM, Mexico City 04510, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4470-9399","authenticated-orcid":false,"given":"R.","family":"Caballero-Cruz","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, UNAM, Mexico City 04510, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Plato, R. 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