Budak, HuseyinErgun, Busra Betul2025-10-112025-10-1120251687-2770https://doi.org/10.1186/s13661-025-02026-6https://hdl.handle.net/20.500.12684/21725In this paper, we first introduce the multiplicative conformable left and right fractional integrals, followed by the derivation of key properties, such as integrability, boundedness, continuity, and the semi-group property, for the newly defined multiplicative conformable fractional integrals. Then, we establish the Hermite-Hadamard inequalities in three distinct senses for multiplicative conformable fractional integrals. Moreover, we present several corresponding midpoint and trapezoidal inequalities for the obtained Hermite-Hadamard inequalities including multiplicative conformable fractional integrals. By special cases, we present the relations between newly obtained inequalities for multiplicative conformable fractional integrals and existing results for multiplicative Riemann-Liouville fractional integrals and multiplicative integrals. Furthermore, we give some new Hermite-Hadamard type, trapezoid type and midpoint type inequalities or multiplicative Riemann-Liouville fractional integrals. Finally, we give several examples and 3D graphs to illustrate the main results.en10.1186/s13661-025-02026-6info:eu-repo/semantics/openAccessMultiplicative calculusHermite-Hadamard inequalityConformable fractional integralsArticle202512-s2.0-85219599305WOS:001434909300001Q1Q1