Fractional iterative differential equations with boundary conditions via μ -Caputo fractional derivative: existence, uniqueness of a solution and Hyers-Ulam stability

Abstract Fractional iterative differential equations with boundary conditions (FIDEs-wBC) have been mainly studied using the classical Caputo fractional derivative or within the framework of initial value problems. In this paper, we investigate the existence, uniqueness, and Hyers–Ulam stability of solutions for FIDEs-wBC defined by the μ -Caputo fractional derivative. This derivative provides a unified framework that includes several classical fractional derivatives as special cases through suitable choices of the function μ . As a result, this approach allows us to study a broader class of fractional iterative boundary value problems that has not been fully considered in the existing literature. By using the Banach contraction principle and Schauder’s fixed point theorem, we establish results on existence and uniqueness in appropriate function spaces. Several examples are also provided to illustrate the theoretical results.