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This type of problem generalizes several problems recently studied in the literature. Moreover, it allows us to unify conservative and non-conservative dynamical processes in the same model. The dependence of the Lagrangian with respect to the boundaries and a free parameter is effective and transforms the standard Herglotz\u2019s variational problem into a problem of a different nature.<\/jats:p>","DOI":"10.1063\/5.0021373","type":"journal-article","created":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T09:50:08Z","timestamp":1602150608000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter"],"prefix":"10.1063","volume":"61","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 (CIDMA), Department of Mathematics, University of Aveiro , 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3535-3909","authenticated-orcid":false,"given":"Nat\u00e1lia","family":"Martins","sequence":"additional","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro , 3810-193 Aveiro, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2020,10,8]]},"reference":[{"issue":"1","key":"2023071705290410000_c1","first-page":"12","article-title":"The Herglotz variational problem on spheres and its optimal control approach","volume":"7","year":"2016","journal-title":"J. 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