Regular Article
Approximate Solutions, Existence, and Uniqueness of the Cauchy Problem of Fuzzy Differential Equations

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Abstract

The Cauchy problem of fuzzy differential equations is investigated by the use of the concept ofH-differentiability due to M. L. Puri and D. A. Ralescu (J. Math. Anal. Appl.91,1983, 552–558). The existence and uniqueness theorem is obtained for the solution of the Cauchy problemx′(t)=f(t, x(t)),x(t0)=x0, for the fuzzy-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported fuzzy sets inRn, where the functionfsatisfies the generalized Lipschitz condition.

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This work was supported by the National Nature Science Foundation of China.