Existence and Ulam–Hyers stability of ODEs involving two Caputo fractional derivatives

Abstract. In this paper, we study existence of solutions to a Cauchy problem for non-linear ordinary differential equations involving two Caputo fractional derivatives. The existence and uniqueness of solutions are obtained by using monotonicity, continuity and explicit estimation of Mittag-Leffler functions via fixed point theorems. Further, we present Ulam–Hyers stability results by using direct analysis methods. Finally, exam-ples are given to illustrate our theoretical results