Monotonicity analysis for nabla h-discrete fractional Atangana–Baleanu differences

Abstract 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 h Z is proved.