A convexity result for fractional differences

In this brief note we demonstrate that under certain conditions the positivity of the fractional difference Δ0μy(t), for a given function y:N0→R and a number μ∈(2,3), implies the convexity of y. This is given as a special case of a more general result. Finally, as a concrete application of this result we demonstrate that a particular class of fractional boundary value problems has no nontrivial positive solutions.