Summary: For the existence and uniqueness of the solutions of fractional differential equations with two-point boundary value conditions, appropriate assumptions and reasonable upper and lower solutions are defined, and the relevant comparison principles are introduced. The existence and uniqueness of the solution of the linear problem are proved by using the upper and lower solution method and the monotone iterative method, and then the extreme solution of the differential equation of the two-point boundary value problem is obtained, and the existence and uniqueness of the solution are proved. An example is given at the end to illustrate this result.