Haider, WaliChen, HaiboAli, Muhammad AamirShehzadi, AsiaBudak, Huseyin2026-07-012026-07-0120251787-24051787-2413https://doi.org/10.18514/MMN.2025.4854https://hdl.handle.net/20.500.12684/23334In this paper, we prove significant results related to the Hermite-Hadamard inequality for convex functions in the framework of Riemann-Liouville fractional integrals with variable order. Two novel equalities are proved to have new fractional trapezoid and midpoint-type inequalities for the differentiable convex functions. This work provides a computational analysis of these inequalities, with numerical examples for convex functions. Additionally, it is demonstrated that the newly identified inequalities represent a generalisation of the comparable inequalities in the literature.en10.18514/MMN.2025.4854info:eu-repo/semantics/openAccessHermite-Hadamard InequalityRiemann-Liouville Fractional IntegralIntegral InequalitiesArticle2627978122-s2.0-105030232692WOS:001648012400017Q2Q20000-0001-8843-955X