Approximate solutions of impulsive integro-differential equations

Abstract

In this paper, we consider impulsive integro-differential equations in Banach space and we establish the bound on the difference between two approximate solutions. We also discuss nearness and convergence of solutions of the problem under consideration. The impulsive integral inequality of Grownwall type is used to obtain results. Mathematical Subject Classification

Existence Results of Random Impulsive Integrodifferential Inclusions with Time-Varying Delays

“…Differential equations (DEs) with impulses are applied to simulate processes that experience rapid changes at discrete moments that is why the dynamics of impulsive DEs have drawn the interest of many academicians in recent decades (see [1][2][3]). Additionally, generally speaking, impulsive effects emerge as prevalent occurrences in the realm of natural phenomena, induced by sudden disturbances that transpire at precise instances, like in the case of different threshold-based biological models, bursting explosive biological medicine models, and the optimal control model in economics (for more details, see [4,5]).…”

Controllability and Hyers-Ulam Stability of Impulsive Integro-differential Equations in Banach Spaces via Iterative Methods

“…It can be said that they are a generalization of initial value problems. Many phenomena in the real-world such as engineering, medicine, control systems, biological models can be modelled by impulsive integro-differential equations, for examples see, (Lakshmikantham, Bainov, & Simeonov, 1989;Paul,& Anguraj, 2006;Castro, & Ramos, 2009 ;Burton, 2005;Jain, Reddy & Kadam, 2018).…”