Abstract
•Defining the RL fractional differences on hZ in the setting of Atangana Baleanu.•Defining the Caputo fractional differences on hZ in the setting of Atangana Baleanu.•Monotonicity analysis.•Fractional discrete mean value theorem.
In this article, benefiting from the nabla h−fractional functions and nabla h−Taylor polynomials, some properties of the nabla h−discrete version of Mittag-Leffler (h−ML) function are studied. The monotonicity of the nabla h−fractional difference operator with h−ML kernel (Atangana–Baleanu fractional differences) is discussed. As an application, the Mean Value Theorem (MVT) on hZ is proved.