In this paper, we mainly study the existence of solution of fractional differential equations. Firstly, the existence of the maxmum solution and minmum solution of the differential equation are proved by using the fixed point theorem and the monotone iteration method. Secondly, the existence of the solution of the original equation is proved by using the newly constructed differential equation. Finally, the application of the monotone iteration method is given through an example.

In this paper, using the method of upper and lower solutions and fixed point Theorem, consider the existence result of the initial value problem for fractional differential equation of Riemann-Liouville fractional derivative, obtained the existence results for maximal and minimal solutions.