New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel

Abstract

This paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The v-monotonicity definitions, namely v-(strictly) increasing and v-(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with v-monotonicity definitions, we find that the investigated discrete fractional operators will be v(2)-(strictly) increasing or v(2)-(strictly) decreasing in certain domains of the time scale Na:= {a, a + 1, ... }. Finally, the correctness of developed theories is verified by deriving mean value theorem in discrete fractional calculus.