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Herglotz's problems of calculus of variations of this type cannot be solved using the standard theory. Main results of this paper are necessary optimality condition of Euler-Lagrange type, natural boundary conditions and the Dubois-Reymond condition for our non-standard variational problem of Herglotz type. We also prove a necessary optimality condition that arises as a consequence of the Lagrangian dependence of the parameter. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases. In addition, two examples are given in order to illustrate our results.<\/p><\/jats:p>","DOI":"10.3934\/dcdss.2021152","type":"journal-article","created":{"date-parts":[[2021,12,3]],"date-time":"2021-12-03T10:44:32Z","timestamp":1638528272000},"page":"573","source":"Crossref","is-referenced-by-count":2,"title":["A non-standard class of variational problems of Herglotz type"],"prefix":"10.3934","volume":"15","author":[{"given":"Nat\u00e1lia","family":"Martins","sequence":"first","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/dcdss.2021152-1","unstructured":"L. Abrunheiro, L. Machado, N. Martins.The Herglotz variational problem on spheres and its optimal control approach, J. Math. Anal.<\/i>, 7<\/b> (2016), 12-22."},{"key":"key-10.3934\/dcdss.2021152-2","doi-asserted-by":"publisher","unstructured":"R. Almeida, A. B. Malinowska.Fractional variational principle of Herglotz, Discrete Contin. Dyn. Syst. Ser. 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