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A formulation of Noether’s theorem for fuzzy problems of the calculus of variations

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Abstract

The theory of the calculus of variations for fuzzy systems was recently initiated in Farhadinia (Inf Sci 181:1348–1357, 2011), with the proof of the fuzzy Euler–Lagrange equation. Using fuzzy Euler–Lagrange equation, we obtain here a Noether–like theorem for fuzzy variational problems.

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References

  1. Brunt, B.V.: The Calculus of Variations. Springer, Heidelberg (2004)

    Book  MATH  Google Scholar 

  2. Buckley, J.J., Feuring, T.: Introduction to fuzzy partial differential equations. Fuzzy Sets Syst. 105, 241–248 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  3. Kosmann-Schwarzbach, Y.: Les théorèmes de Noether, 2nd edn. With a translation of the original article Invariante Variations probleme, Editions de l Ecole Polytechnique, Palaiseau (2006)

  4. Torres, D.F.M.: Quasi-invariant optimal control problems. Port. Math. (N.S.) 61(1), 97–114 (2004)

    MathSciNet  MATH  Google Scholar 

  5. Torres, D.F.M.: Proper extensions of Noethers symmetry theorem for nonsmooth extremals of the calculus of variations. Commun. Pure Appl. Anal. 3(3), 491–500 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Frederico, G.S.F., Torres, D.F.M.: A formulation of Noethers theorem for fractional problems of the calculus of variations. J. Math. Anal. Appl. 334, 834–846 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hoa, N.V.: Fuzzy fractional functional differential equations under Caputo gH-differentiability. Commun. Nonlinear Sci. Numer. Simul. 22, 1134–1157 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Farhadinia, B.: Necessary optimality conditions for fuzzy variational problems. Inf. Sci. 181, 1348–1357 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fard, O.S., Zadeh, M.S.: Note on “Necessary optimality conditions for fuzzy variational problems”. J. Adv. Res. Dyn. Control Syst. 4(3), 1–9 (2012)

    MathSciNet  Google Scholar 

  10. Fard, O.S., Borzabadi, A.H., Heidari, M.: On fuzzy Euler-Lagrange equations. Ann. Fuzzy Math. Inform. 7(3), 447–461 (2014)

    MathSciNet  MATH  Google Scholar 

  11. Goetschel Jr., R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18(1), 31–43 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  12. Xu, J., Liao, Z., Nieto, J.J.: A class of linear differential dynamical systems with fuzzy matrices. J. Math. Anal. Appl. 368(1), 54–68 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

R. Almeida was supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2013.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Damghan University, Damghan, Iran

    O. S. Fard

  2. Department of Mathematics, Damghan University, Damghan, Iran

    J. Soolaki

  3. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810–193, Aveiro, Portugal

    R. Almeida

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  1. O. S. Fard
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  2. J. Soolaki
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  3. R. Almeida
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Correspondence to O. S. Fard.

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Fard, O.S., Soolaki, J. & Almeida, R. A formulation of Noether’s theorem for fuzzy problems of the calculus of variations. Afr. Mat. 29, 33–46 (2018). https://doi.org/10.1007/s13370-017-0524-6

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  • DOI: https://doi.org/10.1007/s13370-017-0524-6

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