Abstract: Firstly, we proved the existence of positive solutions for a class of nonlinear Riemann-Liouville conformable fractional differential equations by using the properties of Green’s function and Guo-Krasnosel’skii’s fixed point theorem, and obtained that there were at least two positive solutions to the problem. Secondly, based on a comparison principle, we proved the existence of extremal solutions to the problem by using the monotone iterative technique and the method of upper and lower solutions.

Key words: fractional differential equation, monotone iterative technique, extremal solution, fixed point theorem