the existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,1), d^{beta}_{0+}y(t)=gleft(t,x(t),d^{q}_{0+}x(t)right), t in (0,1), x(0)=x'(0)=x''(0)=cdots=x^{(m-2)}(0)=0, x(1)=lambda x(xi) ,0y(0)=y',(0)=y''(0)=cdots=y^{(m-2)},(0)=0, y(1)=lambda y(xi) , 0where m in mathbb{n}, m geq 2,alpha,,beta in (m-1,m) and alpha,beta,p,q,lambda satisfy certain conditions.