{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,22]],"date-time":"2025-07-22T10:59:22Z","timestamp":1753181962781,"version":"3.38.0"},"reference-count":15,"publisher":"SAGE Publications","issue":"14","license":[{"start":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T00:00:00Z","timestamp":1346716800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2013,10]]},"abstract":"<jats:p> The aim of this paper is to generalize the Euler\u2013Lagrange equation obtained by Almeida et al., where fractional variational problems for Lagrangians, depending on fractional operators and depending on indefinite integrals, were studied. The new problem that we address here is for cost functionals, where the interval of integration is not the whole domain of the admissible functions, but a proper subset of it. Furthermore, we present a numerical method, based on Jacobi polynomials for solving this problem. <\/jats:p>","DOI":"10.1177\/1077546312458818","type":"journal-article","created":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T00:17:29Z","timestamp":1346804249000},"page":"2177-2186","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":15,"title":["A generalized fractional variational problem depending on indefinite integrals: Euler\u2013Lagrange equation and numerical solution"],"prefix":"10.1177","volume":"19","author":[{"given":"Ricardo","family":"Almeida","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal"}]},{"given":"Hassan","family":"Khosravian-Arab","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran"}]},{"given":"Mostafa","family":"Shamsi","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran"}]}],"member":"179","published-online":{"date-parts":[[2012,9,4]]},"reference":[{"key":"bibr1-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1177\/1077546307077472"},{"key":"bibr2-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/24\/003"},{"key":"bibr3-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.07.016"},{"key":"bibr4-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.02.028"},{"key":"bibr5-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/41\/9\/095201"},{"key":"bibr6-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30728-0"},{"key":"bibr7-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.12.008"},{"key":"bibr8-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198506720.001.0001"},{"key":"bibr9-1077546312458818","doi-asserted-by":"publisher","DOI":"10.4310\/MAA.2008.v15.n4.a2"},{"key":"bibr10-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1016\/S0034-4877(10)00010-8"},{"volume-title":"(North-Holland Mathematics Studies, Vol. 204)","year":"2006","author":"Kilbas AA","key":"bibr11-1077546312458818"},{"key":"bibr12-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.02.032"},{"key":"bibr13-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.02.022"},{"key":"bibr14-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719598"},{"key":"bibr15-1077546312458818","doi-asserted-by":"publisher","DOI":"10.1007\/b97436"}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546312458818","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1077546312458818","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546312458818","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T05:19:54Z","timestamp":1741065594000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546312458818"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,4]]},"references-count":15,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["10.1177\/1077546312458818"],"URL":"https:\/\/doi.org\/10.1177\/1077546312458818","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"type":"print","value":"1077-5463"},{"type":"electronic","value":"1741-2986"}],"subject":[],"published":{"date-parts":[[2012,9,4]]}}}