A unique solution of the iterative boundary value problem for a second-order differential equation approached by fixed point results

Abstract

The analysis of iterative differential equations is often related to the various applications of calculus, which support all mathematical sciences. These equations are critical when it comes to interpreting the infection models. Furthermore, the inclusion of self-mapping raises the complexity of determining the existence of solutions for the iterative differential equations. This paper considers a particular type of second-order iterative differential equations and uses the Banach fixed point theorem to find the existence and uniqueness of the proposed differential equation’s solution. We discuss the Hyers-Ulam and Hyers-Ulam-Rassias type stability of a solution to the proposed iterative boundary-value problem and present three illustrative examples to support our main results.