Hyers-Ulam-Rassias stability of κ-Caputo fractional differential equations

The paper is connected with the existence of solutions and Hyers-Ulam stability for a class of nonlinear fractional differential equations with κ-Caputo fractional derivative in boundary value problems. The existence and uniqueness results are obtained by utilizing the Banach fixed point theorem and Leray-Schauder nonlinear alternative theorem. In addition, two sufficient conditions to guarantee the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of boundary value problems of fractional differential equations are also presented. Finally, theoretical results are illustrated by two numerical examples.