{
  "id": "1403.3937",
  "version": "v1",
  "published": "2014-03-16T17:54:57.000Z",
  "updated": "2014-03-16T17:54:57.000Z",
  "title": "Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition --- Application to fractional variational problems",
  "authors": [
    "Loïc Bourdin",
    "Tatiana Odzijewicz",
    "Delfim F. M. Torres"
  ],
  "comment": "This is a preprint of a paper whose final and definite form will appear in Differential and Integral Equations, ISSN 0893-4983 (See http://www.aftabi.com/DIE.html). Submitted 19/July/2013; Accepted 16/March/2014",
  "journal": "Differential Integral Equations 27 (2014), no. 7/8, 743--766",
  "categories": [
    "math.OC"
  ],
  "abstract": "We study dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator $K$ and defined on bounded-time intervals. Under assumptions of regularity, convexity and coercivity, we derive sufficient conditions ensuring the existence of a minimizer. Finally, we obtain necessary optimality conditions of Euler-Lagrange type. Main results are illustrated with special cases, when $K$ is a general kernel operator and, in particular, with $K$ the fractional integral of Riemann-Liouville and Hadamard. The application of our results to the recent fractional calculus of variations gives answer to an open question posed in [Abstr. Appl. Anal. 2012, Art. ID 871912; doi:10.1155/2012/871912].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-16T17:54:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "49J05"
    ],
    "keywords": [
      "necessary optimality condition",
      "generalized lagrangian functionals",
      "fractional variational problems",
      "application",
      "study dynamic minimization problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.3937B"
    }
  }
}