Publications
Sort:
Open Access Research Article Issue
Some Hermite-Hadamard-Mercer type inequalities via Atangana-Baleanu-conformable fractional operator
AIMS Mathematics 2026, 11(6): 17937-17950
Published: 15 June 2026
Abstract PDF (243.1 KB) Collect
Downloads:0

This paper investigated new Hermite-Hadamard-Mercer type inequalities associated with an Atangana-Baleanu-conformable fractional integral operator. By combining the structural features of Atangana-Baleanu fractional integrals and conformable kernels, we derived a fractional framework that contained both local and nonlocal effects. A fundamental identity was first established, transforming a symmetric combination of endpoint values and fractional integral terms into a weighted integral involving the first derivative. Based on this identity and Jensen-Mercer's inequality, several new bounds were obtained under convexity assumptions on | f | and | f | q , where q > 1. The results extended known Hermite-Hadamard-Mercer inequalities and reduced to classical or fractional special cases under suitable parameter choices. The proposed approach provided a flexible tool for fractional integral inequalities and related estimates in convex analysis.

Total 1