Positivity and monotonicity results for discrete fractional operators involving the exponential kernel

Abstract

This work deals with the construction and analysis of convexity and nabla positivity for discrete fractional models that includes singular (exponential) kernel. The discrete fractional differences are considered in the sense of Riemann and Liouville, and the υ1-monotonicity formula is employed as our initial result to obtain the mixed order and composite results. The nabla positivity is discussed in detail for increasing discrete operators. Moreover, two examples with the specific values of the orders and starting points are considered to demonstrate the applicability and accuracy of our main results.

Keywords

• discrete fractional calculus
• discrete fractional operators with exponential kernel
• monotonicity
• positivity