Novel Exploration of Topological Degree Method for Non-Instantaneous Impulsive Fractional Integro-Differential Equation through Application of Filtering System

Abstract This paper explores the execution of the topological degree method (TDM) on initial conditions for a non-instantaneous impulsive fractional integro-di erential equation (NIFrIDE). The Laplace transform technique (LTT) is used to obtain the solution representation of the given system. The fundamental objective of this work is to acquire the existence and uniqueness results for a nite- dimensional case of a given dynamical system using the topological degree method and Gronwall's inequality, respectively. We examine two numerical computations for a given non-instantaneous impulsive fractional integro-di erential equation. In addition to discussing the application of a given problem through the ltering system.