LAUSR

A monotonicity-type result for functions $$f\ : \ \mathbb {N}_a\rightarrow \mathbb {R}$$f:Na→R satisfying the sequential fractional difference inequality $$\begin{aligned} \Delta _{1+a-\mu }^{\nu }\Delta _{a}^{\mu }f(t)\ge 0, \end{aligned}$$Δ1+a-μνΔaμf(t)≥0,for $$t\in \mathbb {N}_{2+a-\mu -\nu }$$t∈N2+a-μ-ν, where $$0<\mu <1$$0<μ<1, $$0<\nu <1$$0<ν<1, and $$1<\mu +\nu <2$$1<μ+ν<2, is proved, subject to the restriction that $$\begin{aligned} \mu <2(1-\nu ). \end{aligned}$$μ<2(1-ν).We demonstrate that this result is sharp in the sense that the restriction $$\mu <2(1-\nu )$$μ<2(1-ν) cannot be improved.