{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:52:59Z","timestamp":1775227979077,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CIDMA\u2014Center for Research and Development in Mathematics and Applications"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler\u2013Lagrange equation for this generalized case and providing optimality conditions for extremal curves. We explore problems with integral and holonomic constraints and consider higher-order derivatives, where the fractional orders are free.<\/jats:p>","DOI":"10.3390\/fractalfract9030188","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T12:03:06Z","timestamp":1742299386000},"page":"188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fractional Calculus of Variations for Composed Functionals with Generalized Derivatives"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1305-2411","authenticated-orcid":false,"given":"Ricardo","family":"Almeida","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.egypro.2012.05.201","article-title":"Modelisation of the rheological behavior of viscoelastic materials using the fractional derivatives and transfer technique","volume":"19","author":"AlJarbouh","year":"2012","journal-title":"Energy Procedia"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.colsurfa.2016.12.019","article-title":"A study of the rheological properties of visco-elastic materials using fractional calculus","volume":"516","author":"Majumdar","year":"2017","journal-title":"Colloids Surf. 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