Existence and uniqueness of cauchy problem for fuzzy differential equations under dissipative conditions

The existence theorem of Peano for the fuzzy differential equation, x′(t)=f(t,x(t)),x(t0)=x0 does not hold in general except in the special case where the fuzzy number space (En, D) is finite dimensional [1] or f is assumed to be continuous and bounded [2]. In this paper, the dissipative-type conditions which guarantee the existence theorem for Peano are specified based on the existence theorem of approximate solutions to above Cauchy problem.