4.2 Article

Noether's theorem for fractional variational problems of variable order

Journal

CENTRAL EUROPEAN JOURNAL OF PHYSICS
Volume 11, Issue 6, Pages 691-701

Publisher

DE GRUYTER POLAND SP Z O O
DOI: 10.2478/s11534-013-0208-2

Keywords

variable order fractional integrals; variable order fractional derivatives; fractional variational analysis; Euler-Lagrange equations; Noether's theorem

Funding

  1. FEDER funds through COMPETE Operational Programme Factors of Competitiveness (Programa Operacional Factores de Competitividade)
  2. Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro)
  3. Portuguese Foundation for Science and Technology (FCT - Fundacao para a Ciencia e a Tecnologia) [PEst-C/MAT/UI4106/2011]
  4. COMPETE [FCOMP-01-0124-FEDER-022690]
  5. FCT [SFRH/BD/33865/2009, PTDC/MAT/113470/2009]
  6. Malinowska through the project Information Platform TEWI
  7. European Union under the European Regional Development Fund
  8. European Union [64735-SADCO]
  9. Fundação para a Ciência e a Tecnologia [SFRH/BD/33865/2009] Funding Source: FCT

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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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