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Averaging of fuzzy differential equations with delay

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Nonlinear Oscillations

For fuzzy differential equations with delay, we substantiate the schemes of complete and partial averaging on a finite interval.

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References

  1. L. Zadeh, “Fuzzy sets,” Inform. Contr., 8, 338–353 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  2. M. L. Puri and D. A. Ralescu, “Differential of fuzzy functions,” J. Math. Anal. Appl., 91, 552–558 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  3. O. Kaleva, “Fuzzy differential equations,” Fuzzy Sets Syst., 24, No. 3, 301–317 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  4. O. Kaleva, “The Cauchy problem for fuzzy differential equations,” Fuzzy Sets Syst., 35, No. 3, 389–396 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  5. V. Lakshmikantham, S. Leela, and A. S. Vatsala, “Interconnection between set and fuzzy differential equations,” Nonlin. Analysis, 54, 351–360 (2003).

    Article  MathSciNet  Google Scholar 

  6. S. Seikkala, “On the fuzzy initial value problem,” Fuzzy Sets Syst., 24, No. 3, 319–330 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  7. S. J. Song and C. X. Wu, “Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations,” Fuzzy Sets Syst., 111, 55–67 (2000).

    Article  MathSciNet  Google Scholar 

  8. J. Y. Park and H. K. Han, “Existence and uniqueness theorem for a solution of fuzzy differential equations,” Int. J. Math. Math. Sci., 22, No. 2, 271–279 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  9. R. J. Aumann, “Integrals of set-valued functions,” J. Math. Anal. Appl., 12, 1–12 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Hukuhara, “Intégration des applications mesurables dont la valeur est un compact convexe,” Funkc. Ekvacioj., No. 11, 205–223 (1967).

    Google Scholar 

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Authors and Affiliations

  1. Odessa National University, Odessa, Ukraine

    O. D. Kichmarenko & N. V. Skripnik

Authors
  1. O. D. Kichmarenko
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  2. N. V. Skripnik
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Correspondence to O. D. Kichmarenko.

Additional information

Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 316–328, July–September, 2008.

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Kichmarenko, O.D., Skripnik, N.V. Averaging of fuzzy differential equations with delay. Nonlinear Oscill 11, 331–344 (2008). https://doi.org/10.1007/s11072-009-0034-z

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  • DOI: https://doi.org/10.1007/s11072-009-0034-z

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