EXISTENCE AND HYERS-ULAM STABILITY OF IMPULSIVE DELAY INTEGRO-DIFFERENTIAL EQUATIONS

In recent years, impulsive ordinary differential equations with delay terms have garnered significant attention due to their wide applications in various fields, including mechanics, population dynamics, and nuclear reactor physics. The primary objective of this paper is to establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability for impulsive delay ordinary differential equations by employing a novel generalized Gronwall inequality alongside fixed-point methods and Picard's operator technique. An example is provided to illustrate the stability of impulsive differential equation which is based on a new deep learning framework, and the integral operators are learned using neural networks.