Analysis of convexity results for discrete fractional nabla operators

Abstract

We investigate the relationship between the sign of the discrete fractional difference $({\mathrm{\nabla }}_a^{\nu }f)(t)$ and the convexity of the function $f$ in the case where . We focus on the scenario in which $({\mathrm{\nabla }}_a^{\nu }f)(t)$ satisfies a negative lower bound. Our analytical results are complemented with numerical simulations, the latter providing insight beyond what we are able to produce analytically.