Positive solutions to singular fractional differential system with coupled boundary conditions

•Fractional-order differential system with coupled boundary conditions is investigated.•The existence of positive solutions is obtained under the condition that nonlinearity fi (i = 1,2) is semi-positone.•The results of existence contain not only for positive parameter sufficiently small but also λ sufficiently large.•Two examples can illustrate the main results.

By using the fixed point theory in cone and constructing some available integral operators together with approximating technique, the existence of positive solution for a singular nonlinear semipositone fractional differential system with coupled boundary conditions is established. Two examples are then given to demonstrate the validity of our main results.