Approximate solutions, existence, and uniqueness of the Cauchy problem of fuzzy differential equations (Q1922949)

The authors study the Cauchy problem \(x'(t)= f(t,x(t))\), \(x(t_0)= x_0\) for fuzzy differential equations. First the authors show that if \(x_n(t)\) is a solution to an approximate differential equation and \(x_n(t)\) converges uniformly, then the limit function is a solution to the Cauchy problem. Then they give an existence and uniqueness theorem for a solution to the Cauchy problem, which generalizes the corresponding theorem of \textit{O. Kaleva} [Fuzzy Sets Syst. 24, 301-317 (1987; Zbl 0646.34019)]. (Also submitted to MR).