New Fundamental Results on the Continuous and Discrete Integro-Differential Equations

This work studies certain perturbed and un-perturbed nonlinear systems of continuous discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method Lyapunov–Razumikhin (LRM), uniform asymptotic stability (UAS), (US), integrability boundedness solutions as well exponential (ES) instability are discussed. In this paper, five new theorems a corollary given three numerical applications provided with their simulations. With work, we aim to make contributions theory integro-differential equations.