In this paper, certain Hermite–Jensen–Mercer type inequalities are proved via conformable integrals of arbitrary order. We establish some different and new fractional Hermite–Hadamard–Mercer type inequalities for a differentiable function f whose derivatives in the absolute values are convex.

In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.