Lakhdari, AbdelghaniBudak, HuseyinAwan, Muhammad UzairMeftah, Badreddine2025-10-112025-10-1120241687-2770https://doi.org/10.1186/s13661-024-01909-4https://hdl.handle.net/20.500.12684/21731This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus. By introducing a novel integral identity, we establish a series of Milne-type inequalities for functions possessing extended s-convex first-order derivatives. Subsequently, we present an illustrative example complete with graphical representations to validate our theoretical findings. The paper concludes with practical applications of these inequalities, demonstrating their potential impact across various fields of mathematical and applied sciences.en10.1186/s13661-024-01909-4info:eu-repo/semantics/openAccessKatugampola fractional integral operatorsMilne-type inequalitiesConvex functionsP-functionss-Godunova-Levin functionsExtended s-convex functionsArticle202412-s2.0-85201321171WOS:001291106300002Q1Q1