Some new generalized fractional Hermite-Hadamard-Mercer inequalities through Jensen-Mercer inequality

This paper establishes novel Hermite–Hadamard–Mercer inequalities for [Formula: see text]-Riemann–Liouville fractional integrals using the Jensen–Mercer inequality. The obtained results unify and generalize several existing inequalities for Riemann integrals and standard Riemann–Liouville fractional integrals. Numerical examples confirm that increasing the number of points in the Jensen–Mercer scheme leads to sharper bounds. As an application, we derive a [Formula: see text]-Riemann–Liouville fractional integral identity for differentiable mappings and use it to establish error bounds for numerical integration formulas.