The purpose of this paper is to study a generalized Riemann-Liouville fractional differential equation and system with nonlocal boundary conditions. Firstly, some properties of the Green function are presented, and then establish Lyapunov-type inequalities for a sequential $\psi$-Riemann-Liouville fractional boundary value problem. Also, the existence and uniqueness of solutions are proved by using Banach and Schauder fixed point theorems. Furthermore, the existence and uniqueness of solutions to a sequential nonlinear differential system is established by means of Schauder's and Perov's fixed point theorems. Examples are given to validate the theoretical results.
