Dhanalakshmi Kasinathan, Dimplekumar Chalishajar, Ravikumar Kasinathan, Ramkumar Kasinathan
Abstract This paper is concerned with the Hyers–Ulam stability of the mild solution of a higher-order non-instantaneous impulsive fractional neutral stochastic integro-differential equations involving nonlocal conditions in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory, and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the Hyers–Ulam stability of the mild solution to the stochastic system in the p -moment. An example is also considered for illustrating abstract theoretical result.