Hyers-Ulam stability for boundary value problem of fractional differential equations with κ$$ \kappa $$-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.

Automated summary

The purpose of this paper is to discuss basic results of boundary value problems of fractional differential equations (BVP-FDEs) using the concept of Caputo fractional derivative. The existence and uniqueness of solutions for BVP-FDEs are discussed by utilizing Banach fixed point theorem and Schaefer's fixed point theorem. New sufficient conditions for ensuring the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of BVP-FDEs are also provided.