{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T12:41:45Z","timestamp":1781527305499,"version":"3.54.1"},"reference-count":42,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:00:00Z","timestamp":1730246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"EU","doi-asserted-by":"publisher","award":["P20229RMLB"],"award-info":[{"award-number":["P20229RMLB"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we propose a global numerical method for approximating Caputo fractional derivatives of order \u03b1(D\u03b1f)(y)=1\u0393(m\u2212\u03b1)\u222b0y(y\u2212x)m\u2212\u03b1\u22121f(m)(x)dx,y&gt;0, with m\u22121&lt;\u03b1\u2264m,m\u2208N. The numerical procedure is based on approximating f(m) by the m-th derivative of a Lagrange polynomial, interpolating f at Jacobi zeros and some additional nodes suitably chosen to have corresponding logarithmically diverging Lebsegue constants. Error estimates in a uniform norm are provided, showing that the rate of convergence is related to the smoothness of the function f according to the best polynomial approximation error and depending on order \u03b1. As an application, we approximate the solution of a Volterra integral equation, which is equivalent in some sense to the Bagley\u2013Torvik initial value problem, using a Nystr\u00f6m-type method. Finally, some numerical tests are presented to assess the performance of the proposed procedure.<\/jats:p>","DOI":"10.3390\/axioms13110750","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T13:09:27Z","timestamp":1730466567000},"page":"750","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Global Method for Approximating Caputo Fractional Derivatives\u2014An Application to the Bagley\u2013Torvik Equation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0173-5848","authenticated-orcid":false,"given":"Maria Carmela","family":"De Bonis","sequence":"first","affiliation":[{"name":"Department of Basic and Applied Sciences, University of Basilicata, Viale dell\u2019Ateneo Lucano 10, 85100 Potenza, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9446-4452","authenticated-orcid":false,"given":"Donatella","family":"Occorsio","sequence":"additional","affiliation":[{"name":"Department of Basic and Applied Sciences, University of Basilicata, Viale dell\u2019Ateneo Lucano 10, 85100 Potenza, Italy"},{"name":"National Research Council (C.N.R.) of Italy, Institute for Applied Computing (IAC) \u201cMauro Picone\u201d, Via P. 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