Hyers-Ulam stability for boundary value problem of fractional differential equations with kappa$$ \kappa $$-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 alpha is an element of(1,2)$$ \alpha \in \left(1,2\right) $$. 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.