Abstract
For fuzzy fractional functional evolution equations, the concept of global and local existence and uniqueness will be presented in this work. We employ the contraction principle and successive approximations for global and local existence and uniqueness,
respectively, as given{(C)(0)D(9)(H)x (I) = f(I, x(I)) + integral(I)(0) g(I, s, x(s))ds, I >= I-0, I is an element of [0,T], x(I) = psi(I-I-0) = psi(0) is an element of C-sigma,C- I-0 >= I >= I-0 - sigma, where C-sigma denotes the set of fuzzy cotinuous x' (I) = psi' (I) = psi(1),
mapping defined on [I-0 - sigma, T] and sigma > 1. We also use this method to solve fuzzy fractional functional evolution equations with fuzzy population models and distributed delays using fuzzy fractional functional evolution equations. To explain these results, some theorems are given. Finally, certain fuzzy fractional functional evolution equations are illustrated.