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Noether’s theorem for fractional variational problems of variable order

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Central European Journal of Physics

Abstract

We prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

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Author information

Authors and Affiliations

  1. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Tatiana Odzijewicz & Delfim F. M. Torres

  2. Faculty of Computer Science, Bialystok University of Technology, 15-351, Białystok, Poland

    Agnieszka B. Malinowska

Authors
  1. Tatiana Odzijewicz
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  2. Agnieszka B. Malinowska
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  3. Delfim F. M. Torres
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Correspondence to Delfim F. M. Torres.

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Odzijewicz, T., Malinowska, A.B. & Torres, D.F.M. Noether’s theorem for fractional variational problems of variable order. centr.eur.j.phys. 11, 691–701 (2013). https://doi.org/10.2478/s11534-013-0208-2

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  • DOI: https://doi.org/10.2478/s11534-013-0208-2

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