Study on existence and stability analysis for implicit neutral fractional differential equations of ABC derivative

Abstract

In this paper, we study the existence, uniqueness, and stability analysis of non-linear implicit neutral fractional differential equations involving the Atangana–Baleanu derivative in the Caputo sense. The Banach contraction principle theorem is employed to establish the existence and uniqueness of solutions, while Krasnoselskii’s fixed-point theorem is utilized to further analyze the existence of solutions. Stability analysis is also examined, including results for Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias stability. Finally, an example is presented to illustrate the existence and uniqueness of solutions, along with a discussion on their stability.