{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T14:10:11Z","timestamp":1717596611296},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"10","license":[{"start":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T00:00:00Z","timestamp":1380585600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Gr\u00fcnwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.<\/jats:p>","DOI":"10.2478\/s11534-013-0250-0","type":"journal-article","created":{"date-parts":[[2013,5,28]],"date-time":"2013-05-28T03:00:34Z","timestamp":1369710034000},"page":"1262-1267","source":"Crossref","is-referenced-by-count":3,"title":["A discrete time method to the first variation of fractional order variational functionals"],"prefix":"10.2478","volume":"11","author":[{"given":"Shakoor","family":"Pooseh","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal"}]},{"given":"Ricardo","family":"Almeida","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal"}]},{"given":"Delfim","family":"Torres","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal"}]}],"member":"374","published-online":{"date-parts":[[2013,12,19]]},"container-title":["Open Physics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.2478\/s11534-013-0250-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.2478\/s11534-013-0250-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/s11534-013-0250-0\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/s11534-013-0250-0\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T13:48:23Z","timestamp":1717595303000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/s11534-013-0250-0\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,1]]},"references-count":0,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2013,12,19]]},"published-print":{"date-parts":[[2013,10,1]]}},"alternative-id":["10.2478\/s11534-013-0250-0"],"URL":"https:\/\/doi.org\/10.2478\/s11534-013-0250-0","relation":{},"ISSN":["2391-5471"],"issn-type":[{"value":"2391-5471","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,1]]}}}