Existence Of Solutions Of Fractional Differential Equations With Integral Boundary Conditions

In this paper, we study the existence of solutions to a class of fractional differential equations with integral boundary conditions by the fixed point theorems in the cone.The thesis contains four chapters. The first chapter mainly introduce the background, the output of the precious research, and some basic definitions and theorems. In the second chapter, we discuss the existence and uniqueness for a fractional differential equation with integral boundary condition depending on a parameter and receive the existence and uniqueness of solution utilizing the first eigenvalue and the first eigenfunction of the operator. Meanwhile, using the fixed point theory for the sum operator, we obtain the same conclusion. In the third chapter,we discuss the existence of solution to a class of fractional p-Laplacian differential equation with two integral boundary conditions by using the monotone iteration. In chapter four, we discuss the fractional differential equation with Stieltjes integral boundary condition on the infinity interval, and obtain the existence of this equation and the range of this solution by Leray-Schauder theorem. Moreover, we prove the existence of positive solution to the problem by Banach mapping theorem.