Milne’s Estimates via Conformable Fractional Multiplicative Integrals
Universal Journal of Mathematics and Applications, vol.9, no.1, pp.1-18, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 9 Issue: 1
- Publication Date: 2026
- Doi Number: 10.32323/ujma.1767392
- Journal Name: Universal Journal of Mathematics and Applications
- Journal Indexes: Scopus, Central & Eastern European Academic Source (CEEAS), Directory of Open Access Journals
- Page Numbers: pp.1-18
- Keywords: Conformable fractional multiplicative integrals, Functions with bounded ∗-derivatives, Milne’s rule, Multiplicative calculus, Multiplicative convexity
- Open Archive Collection: AVESIS Open Access Collection
- Kocaeli University Affiliated: Yes
Abstract
This paper explores Milne’s inequality in the context of multiplicative conformable fractional integrals, a recent extension of classical fractional calculus rooted in non-Newtonian analysis. Leveraging recent developments in multiplicative calculus, we establish a new fundamental identity that underpins the derivation of Milne-type inequalities for two classes of functions: (i) those whose ∗-derivatives in ∗-absolute value are multiplicative convex, and (ii) those with bounded ∗-derivatives. A numerical example, accompanied by graphical illustrations, is included to demonstrate the validity and effectiveness of the theoretical findings. Further, we extend our analysis to functions satisfying specific derivative constraints and present some applications to special means. The paper concludes with a summary of the main contributions and a discussion of promising avenues for future research in multiplicative fractional analysis.