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A convexity result for fractional differences. (English) Zbl 1314.26010

Summary: In this brief note we demonstrate that under certain conditions the positivity of the fractional difference \(\varDelta_0^\mu y(t)\), for a given function \(y : \mathbb{N}_0 \to \mathbb{R}\) and a number \(\mu \in(2, 3)\), 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.

MSC:

26A33 Fractional derivatives and integrals
39A12 Discrete version of topics in analysis
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