Hyers–Ulam stability analysis of delayed quaternion‐valued neural networks with Caputo–Fabrizio derivative

Abstract This paper explores the problem of analyzing the Hyers–Ulam stability of quaternion‐valued neural networks incorporating time‐varying delays through the utilization of the Caputo–Fabrizio fractional differential operator. A lemma has been generalized from the existing results which will be used to establish the desired stability behavior. We examine the existence and uniqueness of the solution for the considered quaternion‐valued neural networks by employing Banach and Darbo's fixed point techniques. Furthermore, we evaluate the Hyers–Ulam stability behavior of our model within the framework of the Caputo–Fabrizio fractional operator by establishing some sufficient conditions. Lastly, two numerical examples have been presented to validate the stability of the proposed model by demonstrating the effectiveness of the derived results.