Ulam stability of fractional ψ-Caputo differential equations involving two orders for fractional derivatives

Abstract

In this study, we investigate a class of fractional ?-Caputo differential equations with nonlocal boundary integral conditions, focusing on the existence and uniqueness of solutions. Our analysis employs standard fixed point theorems, specifically Banach?s and Krasnoselskii?s fixed point theorems. Additionally, various types of Ulam stability are examined, including Ulam-Hyers stability and Ulam-Hyers-Rassias stability. An illustrative example is provided to demonstrate the validity of the theoretical results.