{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T02:56:36Z","timestamp":1762052196932,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T00:00:00Z","timestamp":1652572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"The Portuguese Foundation for Science and Technology (FCT\u2014Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia)","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020 (CIDMA)"],"award-info":[{"award-number":["UIDB\/04106\/2020 (CIDMA)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We prove a new Taylor\u2019s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor\u2019s and mean value theorems for Caputo\u2013Fabrizio, Atangana\u2013Baleanu\u2013Caputo (ABC) and weighted ABC derivatives.<\/jats:p>","DOI":"10.3390\/axioms11050231","type":"journal-article","created":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T09:48:22Z","timestamp":1652608102000},"page":"231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Taylor\u2019s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8412-7783","authenticated-orcid":false,"given":"Houssine","family":"Zine","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3604-3841","authenticated-orcid":false,"given":"El Mehdi","family":"Lotfi","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8435-5981","authenticated-orcid":false,"given":"Noura","family":"Yousfi","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M\u2019sik, Hassan II University of Casablanca, P.O. Box 7955, Sidi Othman, Casablanca 20000, Morocco"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"501","DOI":"10.2478\/s13540-013-0031-x","article-title":"What Euler could further write, or the unnoticed \u201cbig bang\u201d of the fractional calculus","volume":"16","author":"Podlubny","year":"2013","journal-title":"Fract. Calc. Appl. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3431","DOI":"10.1038\/srep03431","article-title":"Measuring memory with the order of fractional derivative","volume":"3","author":"Du","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_3","first-page":"431","article-title":"Interpretation of fractional derivatives as reconstruction from sequence of integer derivatives","volume":"151","author":"Tarasov","year":"2017","journal-title":"Fund. 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