Hyers-Ulam stability for boundary value problem of fractional differential equations with κ-Caputo fractional derivative

The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) via the concept of Caputo fractional derivative with respect to another function with the order . The existence and uniqueness results of a solution for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. We also provide new sufficient conditions to guarantee the Hyers-Ulam stability and the Hyers–Ulam–Rassias stability of BVP-FDEs. Furthermore, some concrete examples to consolidate the obtained results are also considered.