Approximation results for abstract inverse problem in impulsive differential equation

In this article, we address the approximation of solutions for an inverse problem associated with an abstract differential equation incorporating non-instantaneous impulsive effects. By utilizing the Fredholm equation of the second kind, semigroup theory, semi-discretization technique, and finite difference schemes, we derive an approximate solution. Our approach establishes the equivalence between the original inverse problem and the Fredholm equation, and demonstrates the existence of a solution to the inverse problem. Furthermore, we explore several approximation results. Finally, we provide an illustrative example to highlight the main findings.