Benaissa, BouharketAzzouz, NoureddineBudak, Huseyin2024-08-232024-08-2320241687-2770https://doi.org/10.1186/s13661-024-01889-5https://hdl.handle.net/20.500.12684/14053We use a new function class called B-function to establish a novel version of Hermite-Hadamard inequality for weighted psi-Hilfer operators. Additionally, we prove two new identities involving weighted psi-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h.en10.1186/s13661-024-01889-5info:eu-repo/semantics/openAccessFractional conformable integralsFractional conformable derivativeHermite-Hadamard inequalityHermite-HadamardIntegralsArticle202412-s2.0-85196173634WOS:001250539700001Q3N/A