β-Ulam stability results for Atangana–Baleanu–Caputo fractional equations with non-instantaneous impulsive boundary conditions

Abstract

Numerous fixed point theorems (FPTs) are crucial for scientific research in the domains of engineering and science. The main goal of this article is to examine the $\beta$-Ulam-Hyers stability for non-instantaneous impulsive fractional integro-differential equations with Atangana–Baleanu–Caputo ($\mathrm{AB}$-Caputo) fractional derivative in a Banach space. Moreover, Banach Contraction Mapping Principle (BCMP) and Krasnoselskii fixed point theorems (KFPT) are utilized to prove the uniqueness and existence theorems. At the end, an example is discussed to validate the analytical result. Thus, we generalize a number of previous results.