Application of Schauder fixed point theorem to a coupled system of differential equations of fractional order

In this paper, by using Schauder fixed point theorem, we study the existence of at least one positive solution to a coupled system of fractional boundary value problems given by { -D(0+)(v1)y(1)(t) = lambda(1)a(1)(t)f(t,y(1)(t),y(2)(t) + e(1)(t), -D(0+)(v2)y(2)(t) = lambda(2)a(2)(t)g(t,y(1)(t),y(2)(t)) + e(2)(t), where v(1), v(2) epsilon (n - 1,n] for n > 3 and n epsilon N, subject to the boundary conditions y(1)((i))(0) = 0 = y(2)((i))(0), for 0 <= i <= n - 2, and [D(0+)(alpha)y(1)(t)](t=1) = 0 = [D(0+)(alpha)y(2)(t)](t=1), for 1 <= alpha <= n - 2.