LAKHDARI Abdelghani (Co-Auteur)2025-09-172025-09-172023http://41.111.199.50:4000/handle/123456789/850https://doi.org/10.3390/fractalfract7020166 2023, 7, 166This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications, some error estimates for the Milne-type quadrature formula and new inequalities for the generalized arithmetic and p-Logarithmic means are derived. This paper’s findings represent a significant improvement over previously published results. The paper’s ideas and formidable tools may inspire and motivate further research in this worthy and fascinating field.enArticle