It is well known that lots of practical problems can be described by the models of fractional differential equations, and the fractional calculus and fractional differential equations are important mathematical tools in dealing the practical problems. By using the contraction mapping principle, Krasnoselskii fixed-point theorem and noncompact measure theory, a class of multi-term fractional differential equations with mixed boundary condition is studied, and some existence and uniqueness results under different conditions to the nonlinear term are obtained. These results generalize the existence theorems for the classical Bagley-Torvik equation and some related models.