Analysis and Solutions for First-Order Multi- Integro- Differential Impulsive Equations

Abstract

In this paper the existence and uniqueness of first order multi-integro –multi impulsive equation has been presented in details and explained their approach depended on some inequalities and estimations and some special functions as estimators also, all these provided for interesting results that will presented in all. The problem formulation was presented as a first time with their suitable extension formulation with some conditions depended on provided first order multi-integro –multi impulsive problem. The nonlinear analytic of impulsive differential ordinary equations and definition of generalized \beta-Ulam- Hyers -Rassias stable are used as a basis to establish technical of proving as well as a fixed-point theorem have been used for existence and stability with some interesting estimators for this type of stability to grantee the trajectory to be stable as well as the impulsive analytic and their extension of the proposal first order multi-integro –multi impulsive problem are presented in this issue and given how all these concepts work together. The perturbed impulsive part is presented in this problem as a first time. Also, some illustrative examples have been presented in details to explain how is the results satisfies and true.

Keywords

• Impulsive Integro-Differential, Stability, Existence, Uniqueness