Initial value problem for fuzzy differential equations under dissipative conditions

Information Sciences

Volumn 178, Issue 23, 2008, Pages 4523-4533

  Lupulescu, Vasile ^a  

^a Universitatea Constantin Brancusi din Targu Jiu   (Romania)

Author keywords

Dissipative conditions; Existence and uniqueness theorem; Fuzzy differential equation; Inner product; Stability criteria; Stability result

Indexed keywords

INITIAL VALUE PROBLEMS;

DISSIPATIVE CONDITION; EXISTENCE AND UNIQUENESS THEOREM; FUZZY DIFFERENTIAL EQUATIONS; INNER PRODUCT; STABILITY RESULTS;

STABILITY CRITERIA;

EID: 52949097628     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2008.08.005     Document Type: Article

References (33)

1. Bede B., Rudas I.J., and Bencsik A.L. First order linear fuzzy differential equations under generalized differentiability. Information Sciences 177 (2007) 1648-1662
2. Bede B., and Gal S.G. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems 151 (2005) 581-599
3. Buckley J.J., and Feuring T.H. Fuzzy differential equations. Fuzzy Sets and Systems 110 (2000) 43-54
4. Diamond P., and Kloden P. Metric Spaces of Fuzzy Sets (1994), World Scientific, Singapore
5. Diamond P. Stability and periodicity in fuzzy differential equations. IEEE Transactions on Fuzzy Systems 8 (2000) 583-590
6. Ding Z., Ming M., and Kandel A. Existence of solutions of fuzzy differential equations with parameters. Information Sciences 99 (1997) 205-217
7. Fei W.Y. A generalization of Bihari's inequality and fuzzy random differential equations with non-Lipschitz coefficients. International Journal of Uncertainty, Fuzziness, Knowledge-Bases Systems 15 (2007) 425-439
8. Fei W.Y. Existence and uniqueness of solution for fuzzy differential equations with non-Lipschitz coefficients. Information Sciences 177 (2007) 4329-4337
9. Hullermeier E. An approach to modeling an simulation of uncertain dynamical systems. International Journal of Uncertainty, Fuzziness, Knowledge-Bases Systems 5 (1997) 117-137
10. Kaleva O. Fuzzy differential equations. Fuzzy Sets and Systems 24 (1987) 301-317
11. Kaleva O. The Cauchy problem for fuzzy differential equations. Fuzzy Sets and Systems 35 (1990) 389-396
12. Kaleva O. A note on fuzzy differential equations. Nonlinear Analysis 64 (2006) 895-900
13. Lakshmikantham V., and Leea S. Nonlinear Differential Equations in Abstract Spaces (1981), Pergamon Press, Oxford
14. Lakshmikantham V., and Mohapatra R.N. Theory of Fuzzy Differential Equations and Inclusions (2003), Taylor and Francis Publishers, London
15. Lakshmikantham V., and Leea S. Stability theory of fuzzy differential equations via differential inequalities. Mathematical Inequalities and Applications 2 (1999) 551-559
16. Lakshmikantham V., Gnana Bhaskar T., and Vasundhara Devi J. Theory of Set Differential Equations in Metric Spaces (2006), Cambridge Scientific Publishers, Cambridge
17. Mizukoshi M.T., Barros L.C., Chalco-Cano Y., Román-Flores H., and Bassanezi R.C. Fuzzy differential equations and the extension principle. Information Sciences 177 (2007) 3627-3635
18. Negoita C.V., and Ralescu D.A. Applications of Fuzzy Sets to System Analysis (1975), Birkhauser, Basel
19. Nieto J.J. The Cauchy problem for continuous fuzzy differential equations. Fuzzy Sets and Systems 102 (1999) 259-262
20. Nieto J.J., and Rodriguez-Lopez R. Bounded solutions for fuzzy differential and integral equations. Chaos, Solitons & Fractals 27 (2006) 1376-1386
21. Nieto J.J., Rodriguez-Lopez R., and Franco D. Linear first-order fuzzy differential equations. International Journal of Uncertainty, Fuzziness, Knowledge-Bases Systems 14 (2006) 687-709
22. Park J.Y., and Han H.K. Fuzzy differential equations. Fuzzy Sets and Systems 110 (2000) 69-77
23. Park J.Y., Jung I.H., and Lee M.J. Almost periodic solutions of fuzzy systems. Fuzzy Sets and Systems 119 (2001) 367-373
24. Puri M.L., and Ralescu D.A. Fuzzy random variables. Journal of Mathematical Analysis and Applications 114 (1986) 409-422
25. Puri M.L., and Ralescu D.A. Differentials for fuzzy functions. Journal of Mathematical Analysis and Applications 91 (1983) 552-558
26. Rådström H. An embedding theorem for spaces of convex set. Proceedings of the American Mathematical Society 3 (1952) 165-169
27. Seikkala S. On the fuzzy initial value problem. Fuzzy Sets and Systems 24 (1987) 319-330
28. Song S.J., Guo L., and Feng C.H. Global existence of solutions of fuzzy differential equations. Fuzzy Sets and Systems 115 (2000) 371-376
29. Song S.J., and Wu C. Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations. Fuzzy Sets and Systems 110 (2000) 55-67
30. Song S.J., Wu C., and Xue X.P. Existence and uniqueness of Cauchy problem for fuzzy differential equations under dissipative conditions. Computers and Mathematics with Applications 51 (2006) 1483-1492
31. Wu C., and Song S.J. Approximate solutions existence and uniqueness of the Cauchy problem of fuzzy differential equations. Journal of Mathematical Analysis and Applications 202 (1996) 629-644
32. Wu C.X., and Song S.J. Existence theorem to the Cauchy problem of fuzzy differential equations under compactness-type conditions. Information Sciences 108 (1998) 123-134
33. Xue X.P., and Fu Y.Q. On the structure of solutions for fuzzy initial value problem. Fuzzy Sets and Systems 157 (2006) 212-222