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In this paper, we present the Hyers–Ulam stability and Hyers–Ulam-Rassias stability (HU-stability and HUR-stability for short) for fuzzy initial value problem (FIVP) by using fixed point theorem. We improve and extend some known results on the stability for FDEs by dropping some assumptions. Some examples illustrate the theoretical results.

This paper is devoted to studying the maximal and minimal solutions for the interval-valued functional integro- differential equations (IFIDEs) under generalized Hukuhara differentiability by the method of upper and lower solutions and monotone iterative technique. Some examples are given to illustrate the results.

In this paper, we establish the global existence and uniqueness results for fuzzy functional differential equations (FFDEs) by using two different methods. We have extended and generalized some comparison theorems and stability theorem for FFDEs with definition a new Lyapunov-like function. Some examples are given to illustrate these results.

In this paper, we consider the random fuzzy integro-differential equations (RFIDEs) under generalized H- differentiability. The local existence of solutions for RFIDEs with initial conditions under generalized H-differentiability is studied. Two theorems for local existence of solutions are given and proved. Some examples are given to illustrate these results.

In this paper, we prove the existence and uniqueness results for the random fuzzy functional integro-differential equations under generalized Hukuhara differentiability. For the existence and uniqueness, we use the method of successive approximations. Some kinds of boundedness of the solution are established. Moreover, we provide examples to illustrate the results.