Lemma 1: Let [upsilon], w [member of] E and 5 scalar, then for r [member of] (0,1] [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Fuzzy Cauchy Problem Consider the fuzzy initial value problem [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6) where f is a continuous mapping from [R.

Kaleva showed in [18; 19] that if continuous and satisfies the Lipschitz condition with respect to u , then there exists a unique local solution for the fuzzy initial value problem u'(t) = f (t,u), u(0) = [u.

Fuzzy Initial Value Problem Consider a first-order fuzzy initial value fuzzy differential equation given by {y'(t) = g (t, y (t)), t [member of] [0,1] y ([t.