Budak, HuseyinOzmen, Nejla2025-10-112025-10-1120251687-2770https://doi.org/10.1186/s13661-025-02096-6https://hdl.handle.net/20.500.12684/21720In this paper, we first establish the Hermite-Hadamard inequality for left fractional conformable integral operators. Then, we present an example and a graph to illustrate the obtained Hermite-Hadamard inequalities. Moreover, we also present several corresponding trapezoid and midpoint inequalities. For this aim, we first prove two identities for differentiable functions. By using these equalities, we establish some trapezoid- and midpoint-type inequalities for convex functions. Furthermore, we present several remarks to give the relation between the obtained results in this paper and earlier ones.en10.1186/s13661-025-02096-6info:eu-repo/semantics/closedAccessBeta functionFractional conformable integral operatorsHermite-Hadamard-type inequalitiesIncomplete beta functionArticle202512-s2.0-105011077294WOS:001531125900001Q1Q1