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Abstract
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This study deals with a novel class of mean-type inequalities by employing fractional
calculus and convexity theory. The high correlation between symmetry and convexity increases its
significance. In this paper, we first establish an identity that is crucial in investigating fractional
mean inequalities. Then, we establish the main results involving the error estimation of the Hermite–
Hadamard inequality for composite convex functions via a generalized Riemann-type fractional
integral. Such results are verified by choosing certain composite functions. These results give wellknown
examples in special cases. The main consequences can generalize many known inequalities
that exist in other studies.
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