Jensen-Mercer variant of Hermite-Hadamard type inequalities via Atangana-Baleanu fractional operator

Abstract

We present new Mercer variants of Hermite-Hadamard (HH) type inequalities via Atangana-Baleanu (AB) fractional integral operators pertaining non-local and non-singular kernels. We establish trapezoidal type identities for fractional operator involving non-singular kernel and give Jensen-Mercer (JM) variants of Hermite-Hadamard type inequalities for differentiable mapping Υ possessing convex absolute derivatives. We establish connections of our results with several renowned results in the literature and also give applications to special functions.

Keywords

• jensen-mercer inequality
• atangana-baleanu fractional operators
• q-digamma function
• convex function