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