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 { −D1 0+ y1(t) = λ1a1(t)f(t, y1(t), y2(t)) + e1(t), −D2 0+ y2(t) = λ2a2(t)g(t, y1(t), y2(t)) + e2(t), where ν1, ν2 ∈ (n− 1, n] for n > 3 and n ∈ N , subject to the boundary conditions y 1 (0) = 0 = y (i) 2 (0), for 0 ≤ i ≤ n− 2, and [Dα 0+y1(t)]t=1 = 0 = [D α 0+y2(t)]t=1, for 1 ≤ α ≤ n− 2.