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 ν-monotonicity definitions, namely ν-(strictly) increasing and ν-(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with ν-monotonicity definitions, we find that the investigated discrete fractional operators will be ν2-(strictly) increasing or ν2-(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.