The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result.

In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

This paper deals with a new class of non-linear impulsive sequential fractional differential equations with multi-point boundary conditions using Caputo fractional derivative, where impulses are non instantaneous. We develop some sufficient conditions for existence, uniqueness and different types of Ulam stability, namely Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability and generalized Hyers–Ulam–Rassias stability for the given problem. The required conditions are obtained using fixed point approach. The validity of our main results is shown with the aid of few examples.