On the Nonlinear Impulsive Volterra-Fredholm Integrodifferential Equations

TL;DR

This paper studies the existence, uniqueness, and data dependence of solutions for nonlinear impulsive Volterra-Fredholm integrodifferential equations, extending integral inequalities and comparing methods for broader applicability.

Contribution

It introduces a new approach using extended integral inequalities to analyze solution properties, requiring fewer restrictions than traditional Picard operator methods.

Findings

Established existence and uniqueness of solutions.

Demonstrated data dependence on initial conditions.

Extended integral inequality for piecewise continuous functions.

Abstract

In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions and on nonlinear functions involved in integrodifferential equations. Further, we extend the integral inequality for piece-wise continuous functions to mixed case and apply it to investigate the dependence of solution on initial data through $\epsilon$-approximate solutions. It is seen that the uniqueness and dependency results got by means of integral inequity requires less restrictions on the functions involved in the equations than that required through Picard operators theory.