Azzouz, NoureddineBenaissa, BouharketBudak, HueseyinDemir, Izzettin2025-10-112025-10-1120251687-2770https://doi.org/10.1186/s13661-025-02001-1https://hdl.handle.net/20.500.12684/21726In this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of psi-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on psi. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and H & ouml;lder's integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann-Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions.en10.1186/s13661-025-02001-1info:eu-repo/semantics/openAccessh-convex functionRiemann-Liouville fractional integralspsi-Hilfer integral operatorHermite-Hadamard-Mercer inequalityArticle202512-s2.0-85218189934WOS:001412868600001Q1Q1