Research On The Existence Of Solutions For Some Class Of Boundary Value Problem Of Nonlinear Fractional Coupled Systems

In the present paper, we focuses on the existence of two types of fractional differential equations with boundary value coupled systems and we obtain the sufficient conditions of the existence of solutions for these two type equations.We divide this article into the following four sections:In the first part, we mainly introduce the development background and history of fractional calculus theory. In addition, the research status of fractional differential equations is also shown in this section.In the second part, some basic concepts and properties of the fractional calculus theory which will be used to prove our main results in the next sections were presented.The third part of the present paper is concerned with a class of a coupled systems of nonlinear fractional order with three-point boundary value problem. By using the properties of the Green’s function and the Schauder fixed point theorem, the existence of this problem was obtained.In the final part, we discuss the another class of nonlinear coupled systems of nonlinear fractional order. By using the properties of the Green’s function and the Banach contraction mapping principle 、Leray-Schauder fixed point theorem, we get the existence of solutions for this system.