Positive solutions for a class of boundary value problems with fractional q-differences

In this paper, we investigate the existence of positive solutions to the nonlinear q-fractional boundary value problem (Dαq y)(x) = −f (x, y(x)), 0 < x < 1, y(0) = (Dqy)(0) = 0, (Dqy)(1) = β ≥ 0, by applying a fixed point theorem in cones.