Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives

Abstract

• In this paper, we investigate the boundary value problem with Riemann-Liouville fractional differential equations for a class of impulsive implicit nonlinear fractional order integro-differential equations. • We are using some sufficient conditions to achieve the existence and uniqueness results of the projected model with the help of Banach contraction principle, Schauder’s fixed point theorem and Kranoselskii’s fixed point theorem. • Moreover, we present different types of stability such as Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability using the classical technique of functional analysis. • To illustrate our theoretical results, at the end we give an example. In this article, we investigate the existence, uniqueness, and stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives. We analyze the existence and uniqueness of the projected model with the help of Banach contraction principle, Schauder’s fixed point theorem, and Krasnoselskii’s fixed point theorem. Moreover, we present different types of stability using the classical technique of functional analysis. To illustrate our theoretical results, at the end we give an example.