Hyder, Abd-AllahBudak, HuseyinBarakat, Mohamed A.2024-08-232024-08-2320242473-6988https://doi.org/10.3934/math.2024551https://hdl.handle.net/20.500.12684/13780This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.en10.3934/math.2024551info:eu-repo/semantics/openAccessfractional integralsMilne-type inequalitiesfunctions of bounded variationconvex functionsbounded functionsSimpsons TypeArticle9511228112462-s2.0-85188650862WOS:001189376200002Q2N/A