Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions

• The model we study is much closer to real situation compared to existing research.
• Conditions of solution existence are more easily to be obtained by our method.
• We can get upper and lower solutions more easily by our method.

In this paper, we study the existence of multiple solutions for the integral boundary value problems of fractional differential equations by the method of upper and lower solutions and Leray–Schauder degree theory. The sufficient conditions about the existence of at least three solutions are obtained. Moreover, it is proved that the integral boundary value problem has at least three positive solutions under the conditions of M=0M=0 and f is nonnegative. By given two upper and lower solutions which can be easily obtained through our methods, we can present the existence theorem of at least three solutions. Two examples are also included to illustrate the effectiveness of the proposed results.