On The Theory of Multiplicative Conformable Fractional Integrals and Their Applications to Hermite–Hadamard and Maclaurin-type Inequalities
Fractals, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1142/s0218348x2650132x
- Journal Name: Fractals
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Keywords: GG-Convexity, Hermite–Hadamard Inequality, Maclaurin’s Inequality, Multiplicative Calculus, Multiplicative Conformable Fractional Integrals
- Istanbul Gelisim University Affiliated: Yes
Abstract
This paper introduces multiplicative conformable fractional integrals within the setting of (Formula presented)-calculus, a non-Newtonian framework naturally suited for positive functions with positive arguments. This new operator combines the flexibility of conformable fractional calculus with the multiplicative structure of (Formula presented)-calculus, offering a promising tool for modeling scale-invariant and exponential-type phenomena. We begin by defining the multiplicative conformable integrals. Subsequently, based on iterated multiplicative conformable integrals, we construct the multiplicative conformable fractional integrals and investigate their fundamental properties. Finally, as an application, we establish associated multiplicative Hermite–Hadamard and Maclaurin-type inequalities via (Formula presented)-convexity.