Analysis of Iterative Method for Impulsive Neutral Functional Integro-Differential Equation Using Degree Theory

The fundamental objective of this paper is to develop the impulsive neutral functional integro-differential equation by employing an iterative process to establish comprehensive analytical results. Using the topological degree method, we derive sufficient and necessary conditions for the existence of solutions to the given dynamical system. To further validate these results, we utilize Gronwall's inequality, which plays a crucial role in proving the uniqueness of the solutions under specific conditions. Additionally, numerical computations are provided to illustrate the theoretical findings and to assess their accuracy and applicability. These computations highlight the effectiveness of the proposed method.