Abstract
In this work, the nabla fractional differences of order 0<mu<1 with discrete exponential kernels are formulated on the time scale hZ, where 0<h <= 1. Hence, the earlier results obtained in Adv. Differ. Equ., 2017, (78) (2017) are generalized. The monotonicity properties of the h-Caputo-Fabrizio (CF) fractional difference operator are concluded using its relation with the nabla h-Riemann-Liouville (RL) fractional difference operator. It is shown that the monotonicity coefficient depends on the step h, and this dependency is explicitly derived. As an application, a fractional difference version of the mean value theorem (MVT) on hZ is proved.