{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T16:49:11Z","timestamp":1765039751565,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T00:00:00Z","timestamp":1714608000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Portuguese funds through the CIDMA\u2014Center for Research and Development in Mathematics and Applications and the Portuguese Foundation for Science and Technology (FCT-Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia)","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>In this article, we explore a variety of problems within the domain of calculus of variations, specifically in the context of fractional calculus. The fractional derivative we consider incorporates the notion of weighted fractional derivatives along with derivatives with respect to another function. Besides the fractional operators, the Lagrange function depends on extremal points. We examine the fundamental problem, providing the fractional Euler\u2013Lagrange equation and the associated transversality conditions. Both the isoperimetric and Herglotz problems are also explored. Finally, we conclude with an analysis of the variational problem, incorporating fractional derivatives of any positive real order.<\/jats:p>","DOI":"10.3390\/fractalfract8050272","type":"journal-article","created":{"date-parts":[[2024,5,2]],"date-time":"2024-05-02T07:04:14Z","timestamp":1714633454000},"page":"272","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimizing Variational Problems through Weighted Fractional Derivatives"],"prefix":"10.3390","volume":"8","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":[[2024,5,2]]},"reference":[{"key":"ref_1","first-page":"948","article-title":"On the new fractional derivative and application to nonlinear Fisher\u2019s reaction-diffusion equation","volume":"273","author":"Atangana","year":"2016","journal-title":"Appl. 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