Some novel inequalities involving Atangana-Baleanu fractional integral operators and applications

Abstract

As we know, Atangana and Baleanu developed great fractional integral operators which used the generalized Mittag-Leffler function as non-local and non-singular kernel. Inspired by these integral operators, we derive in this paper two new fractional integral identities involving Atangana-Baleanu fractional integrals. Using these identities as auxiliary results, we establish new fractional counterparts of classical inequalities essentially using first and second order differentiable higher order strongly n-polynomial convex functions. We also discuss several important special cases of the main results. In order to show the efficiency of our main results, we offer applications for special means and for differentiable functions of first and second order that are in absolute value bounded.

Keywords

• atangana-baleanu fractional integrals
• higher order strongly n-polynomial convex
• hölder's inequality
• power mean inequality
• special means
• bounded functions