Abstract
In this paper we analyze the existence and uniqueness of solutions for a fuzzy initial value problem of kind x'(t) = f(t,x(t)), x(t0) = x0, where f: T x X --> X is a fuzzy-valued mapping, T is a time interval, X is a class of fuzzy sets, x0 ∈ X and to ∈ T. We consider x'(t) as a generalization of the Hukuhara derivative.
Keywords
References
Bede B. & Gal S. Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Set and Systems 151 (2005) 581-599.
Chalco-Cano Y. & Román-Flores H. Comparison between some approaches to solve fuzzy differential equations, Fuzzy Set and Systems 160 (2009) 1517-1527.
Chalco-Cano Y. & Román-Flores H. On new solutions of fuzzy differential equations, Chaos Solitons & Fractals 38 (2008) 112-119.
Diamond P. Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations, IEEE Trans. Fuzzy System 7 (1999) 734-740.
Diamond P. Stability and periodicity in fuzzy differential equations, IEEE Trans. Fuzzy System 8 (2000) 583-590.
Hukuhara M. Intégration des applications measurables dont la valeur est un compact convexe, Finacialaj Ekvacioj 10 (1967) 205-223.
Kaleva O. Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987) 301-317.
Khastan, A. & Nieto, J. A boundary value problem for second-order fuzzy differential equations. Nonlinear Anal. 72 (2010) 3583-3593.
Negoita C. & Ralescu D. Applications of Fuzzy Sets to Systems Analysis, Wiley, New York, (1975) 12-31.
Nieto J. The Cauchy problem for continuous fuzzy differential equations, Fuzzy Set and Systems 102 (1999) 259-262.
Park J. & Han H. Existence and uniqueness theorem for solutions of fuzzy differential equations, Internat. J. Math. & Math. Sci. 22 (1999) 271-279.
Puri M. & Ralescu D. Differential of fuzzy functions, J. Math. Anal. Appl. 91 (1983) 552-558.
Puri M. & Ralescu D. Fuzzy random variables, J. Math. Anal. Appl. 114 (1986) 409-422.
Radstrom H. An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952) 165-169.
Song S. & Wu C. Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy Set and Systems 110 (2000) 55-67.
Seikkala S. On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987) 319-330.
Xu, J., Liao, Z. & Nieto, J. A class of linear differential dynamical systems with fuzzy matrices. J. Math. Anal. Appl. 368 (2010) 54-68.
Zadeh L. Fuzzy sets, Information and Control 8 (1965), 338-353.
Zadeh L. Toward a generalized theory of uncertainty (G U T-an outline), Information Sciences 172 (2005) 1-40.
Zhang, D., Feng, W., Zhao, Y. & Qiu, J. Global existence of solutions for fuzzy second-order differential equations under generalized H-differentiability. Computers and Mathematics with Applications, In Press, doi: 10.1016/j.camwa.2010.06.038
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