Fuzzy differential equations with impulses in fixed moment of time (in Russian)

N.V.Scripnik

The paper deals with fuzzy impulsive differential equations. A theorem of continuous dependence of the solutions on the initial data and the right-hand sides is proved.

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3. some11 Kaleva O. The Cauchy problem for fuzzy differential equations // Fuzzy sets and systems. -- 1990. -- V.~35, № 3. -- P. 389--396.

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8. Puri M.L., Ralescu D.A. Fuzzy random variables // J. Math. Anal. Appl. -- 1986. -- V.114, № 2. -- P.~409--422.

9. Seikkala S. On the fuzzy initial value problem // Fuzzy Sets and Systems. -- 1987. -- V. 24, № 3. -- P.~319--330.

10. Song S.J., Wu C.X. Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations // Fuzzy Sets and Systems. -- 2000. -- V. 110. -- P. 55--67.

11. Zadeh L. Fuzzy sets // Inform. and Control. -- 1965. -- № 8. -- P. 338--353.

	Fuzzy differential equations with impulses in fixed moment of time (in Russian)
Author	N.V.Scripnik talie@ukr.net Odesa I.I. Mechnikov National University
Abstract	The paper deals with fuzzy impulsive differential equations. A theorem of continuous dependence of the solutions on the initial data and the right-hand sides is proved.
Keywords	fuzzy differential equation, impulse, fixed moment of time
DOI	doi:10.30970/ms.28.1.51-56
Reference	1. Aumann R.J. Integrals of set--valued functions // J. Math. Anal. Appl. -- 1965. -- № 12. -- P. 1--12. 2. Kaleva O. Fuzzy differential equations // Fuzzy sets and systems. -- 1987. -- V. 24, № 3. -- P. 301--317. 3. some11 Kaleva O. The Cauchy problem for fuzzy differential equations // Fuzzy sets and systems. -- 1990. -- V.~35, № 3. -- P. 389--396. 4. Laksmikantham V., Leela S., Vatsala A.S. Interconnection between set and fuzzy differential equations // Nonlinear Analysis. -- 2003. -- V. 54.-- P. 351--360. 5. Negoita C.V., Ralescu D.A. Applications of fuzzy sets to systems analysis. -- New York, Toronto: John Wiley and Sons, 1975. 6. Park J.Y., Han H.K. Existence and uniqueness theorem for a solution of fuzzy differential equations // Internat. J. Math. and Math. Sci. -- 1999. -- V. 22, № 2. -- P. 271--279. 7. Puri M.L., Ralescu D.A. Differential of fuzzy functions // J. Math. Anal. Appl. -- 1983. -- V. 91. -- P.~552--558. 8. Puri M.L., Ralescu D.A. Fuzzy random variables // J. Math. Anal. Appl. -- 1986. -- V.114, № 2. -- P.~409--422. 9. Seikkala S. On the fuzzy initial value problem // Fuzzy Sets and Systems. -- 1987. -- V. 24, № 3. -- P.~319--330. 10. Song S.J., Wu C.X. Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations // Fuzzy Sets and Systems. -- 2000. -- V. 110. -- P. 55--67. 11. Zadeh L. Fuzzy sets // Inform. and Control. -- 1965. -- № 8. -- P. 338--353.
Pages	51-56
Volume	28
Issue	1
Year	2007
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html