Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions

Abstract

Abstract In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and Leray–Schauder nonlinear alternative. Further, we present Ulam–Hyers stability results by using direct analysis methods. Different types of Ulam stability, such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability, are studied. Examples which support our theoretical results are also presented.

Keywords

• Existence and uniqueness
• Fixed point theorem
• Fractional differential equations
• Conformable integrals
• Conformable derivatives
• Ulam–Hyers stability