In this paper, two types of fixed point theorems are employed to study the
solvability of nonlocal problem for implicit fuzzy fractional differential
systems under Caputo gH-fractional differentiability in the framework of
generalized metric spaces. First of all, we extend Krasnoselskii?s fixed
point theorem to the vector version in the generalized metric space of fuzzy
numbers. Under the Lipschitz conditions, we use Perov?s fixed point theorem
to prove the global existence of the unique mild fuzzy solution in both
types (i) and (ii). When the nonlinearity terms are not Lipschitz, we
combine Perov?s fixed point theorem with vector version of Krasnoselskii?s
fixed point theorem to prove the existence of mild fuzzy solutions. Based on
the advantage of vector-valued metrics and convergent matrix, we attain some
properties of mild fuzzy solutions such as the boundedness, the attractivity
and the Ulam - Hyers stability. Finally, a computational example is
presented to demonstrate the effectivity of our main results.
Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones