This paper investigates the existence of positive solutions for the following high-order nonlinear fractional differential boundary value problem (BVP, for short)

This paper investigates the existence of positive solutions for the following high-order nonlinear fractional differential boundary value problem (BVP, for short) {Dα0+u(t)+f(t,v(t))=0,t∈(0,1), Dα0+v(t)+g(t,u(t))=0,t∈(0,1), u(j)(0)=v(j)(0)=0,0≤j≤n−1,j≠1,u′(1)=λ∫10u(t)d(t),v′(1)=λ∫10v(t)d(t), where n − 1 α ≤ n ; n ≥ 3 ; 0 ≤ λ 2 , D α 0 + is the Caputo fractional derivative. By using the monotone method, the theory of fixed point index on cone for differentiable operators and the properties of Green s function, some new uniqueness and existence criteria for the considered fractional BVP are established. As applications, some examples are worked out to demonstrate the main results.