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Hamilton’s principle with variable order fractional derivatives

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Abstract

We propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler-Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation. Necessary conditions for the existence of the minimizer are obtained. They imply various known results in a special cases.

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Authors and Affiliations

  1. Department of Mechanics, University of Novi Sad, Trg. Dositeja Obradovica 6, 21 000, Novi Sad, Serbia

    Teodor M. Atanackovic

  2. Department of Mathematics and Informatics, University of Novi Sad, Trg. Dositeja Obradovica 4, 21 000, Novi Sad, Serbia

    Stevan Pilipovic

Authors
  1. Teodor M. Atanackovic
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  2. Stevan Pilipovic
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Correspondence to Teodor M. Atanackovic.

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Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

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Atanackovic, T.M., Pilipovic, S. Hamilton’s principle with variable order fractional derivatives. fcaa 14, 94–109 (2011). https://doi.org/10.2478/s13540-011-0007-7

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  • DOI: https://doi.org/10.2478/s13540-011-0007-7

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