@article{Lo2026, 
author = {Jen Chieh Lo},
title = {Some Hermite-Hadamard-Mercer type inequalities via Atangana-Baleanu-conformable fractional operator},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17937-17950},
keywords = {Hermite-Hadamard-Mercer-type inequalities, Atangana-Baleanu fractional operator, conformable fractional operator, integral inequalities, fractional calculus, convex functions},
url = {https://www.sciopen.com/article/10.3934/math.2026731},
doi = {10.3934/math.2026731},
abstract = {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.}
}