A convexity result for fractional differences

In this brief note we demonstrate that under certain conditions the positivity of the fractional difference Δ 0 μ y ( t ) , for a given function y : N 0 → 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.