Monotonicity Analysis of Fractional Proportional Differences

Abstract

In this work, the nabla discrete new Riemann–Liouville and Caputo fractional proportional differences of order 00 then χz is ερ −increasing, and if χz is strictly increasing on ℕc and χc>0, then ∇c−1Rχε,ρz>0. As an application of our findings, a new version of the fractional proportional difference of the mean value theorem (MVT) on ℤ is proved.