Solvability Of Two Types Of Fractional Differential Equations With Integral Boundary Value Conditions

In this paper,we mainly investigate the existence of solutions for the two following fractional differential equations with integral boundary value conditions in the sense of Caputo fractional derivative.Firstly,we study the fractional differential equation with integral boundary value conditions as follows:Where 2<??3,0??<2 are real numbers and f ? C([0,1]×[0,+?),(0,+?)).In this chapter,by using the method of lower and upper solutions combined with Schauder's fixed-point theorem,we obtained the existence of at least one positive solution.Then the suffi-cient conditions for the extremal solutions of this problem are obtained by means of the method of lower and upper solutions combined with monotone iterative technique.Then,we discuss the existence of solutions for the following frac-tional differential equation with integral boundary value conditions:Where 1<??2,M?R and f?C([0,1]×R,R),g ? C([0,1],R).In this chapter,we get the existence of solutions for this fractional differential equation by using the Schaefer's fixed-point theorem and the Leray-Schauder degree respectively.