Some positive results for exponential-kernel difference operators of Riemann-Liouville type

Abstract

We established positivity of $ \nabla{f} $ obtained from a systematic computation of a composition of sequential fractional differences of the function $ {f} $ that satisfy certain conditions in a negative lower bound setup. First, we considered the different order sequential fractional differences in which we need a complicated condition. Next, we equalled the order of fractional differences and we saw that a simpler condition will be needed. We illustrated our positivity results for an increasing function of the rising type.

Keywords

• riemann-liouville fractional operators
• exponential kernel
• positivity analyses
• negative lower bound