Hyers-Ulam stability for nonlocal fractional partial integro-differential equation with uncertainty

In this paper, we study nonlocal problems for fractional partial intergro-differential equations with uncertainty in the framework of partially ordered generalized metric spaces of fuzzy valued functions. Based on generalized contractive-like property over comparable items, which is weaker than the Lipschitz condition, we prove the global existence of mild solutions on the infinite domain J∞ = [0, ∞) × [0, ∞). Moreover, Hyers-Ulam stability of this problem is given with the help of Perov-like fixed point theorem.