In this paper, we study the existence of solutions for fractional differential equations with the Caputo-Hadamard fractional derivative of order α ∈ (1, 2]. The uniqueness result is proved via Banach's contraction mapping principle and the existence results are established by using the Schauder's fixed point theorem. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability of the proposed equation is employed. Some examples are given to illustrate the results.