Existence Uniqueness Of Solutions For Singular Nonlinear Systems Of Fractional Differential Equations

With the wide application of the fractional differential equations, the existence and uniqueness of the solutions are also studied extensively. In this paper, we first introduce the background of the fractional differential equa-tion. In the second chapter, we list some basic concepts of fractional order equations. In the third and four chapter, we discuss the existence and unique-ness of the solutions of the following two equation systems based on the research results of Mohamed jleli[4]and Su[13]. The first equation system is which 0< αi≤1,0<mi≤α1,0<ni≤α2, i=1,2, u(0)=v(0)=0,0≤t≤ a, a>1,Dαi are Riemann-Liouville fractional differential equations. Based on a coupled fixed point theorem on ordered metric spaces discussing the solution.The second equation system is which 0<αi≤1,0< mi≤α1,0<ni<α2,i= 1,2, u(0)=v(0)= 0,0≤ t≤a,a>1,Dαi are Riemann-Liouville fractional differential equations. Ap-plying the Schauder fixed point theorem and Banach fixed point theorem, we get the existence and uniqueness results.