Analysis of positivity results for discrete fractional operators by means of exponential kernels

Abstract

In this study, we consider positivity and other related concepts such as α−convexity and α−monotonicity for discrete fractional operators with exponential kernel. Namely, we consider discrete Δ fractional operators in the Caputo sense and we apply efficient initial conditions to obtain our conclusions. Note positivity results are an important factor for obtaining the composite of double discrete fractional operators having different orders.

Keywords

• discrete fractional calculus
• discrete cf-fractional operators
• monotonicity analyses