In this study, we have presented two new alternative definitions corresponding to the basic
definitions of the discrete delta and nabla fractional difference operators. These definitions …

In this study, we consider the analysis of monotonicity for the Riemann-Liouville fractional
differences of sequential type. The results are defined on the subsets of (0, 1)×(0, 1) with a …

This paper deals with studying monotonicity analysis for discrete fractional operators with
Mittag-Leffler in kernel. The ν-monotonicity definitions, namely ν-(strictly) increasing and ν …

We consider the positivity of the discrete sequential fractional operators (RL a0+ 1∇ ν1
defined on the set D1 (see (1.1) and Figure 1) and (RL a0+ 2∇ ν1 RL a0∇ ν2 f)(τ) RL a0∇ …

In this paper we study the positivity analysis problems for discrete fractional operators with
exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied …

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 …

We study the monotonicity method to analyse nabla positivity for discrete fractional operators
of Riemann-Liouville type based on exponential kernels, where (CFR c0 r∇ F)(t)>-ϵ λ (θ-1) …

In this paper, we will discuss the monotone decreasing and increasing of a discrete
nonpositive and nonnegative function defined on Nr0+ 1, respectively, which come from …

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 …