ON MULTIPLICATIVE FRACTIONAL OPERATORS OF HADAMARD AND KATUGAMPOLA TYPES IN G-CALCULUS AND RELATED HERMITE–HADAMARD INEQUALITIES
Fractals, vol.34, no.9, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 9
- Publication Date: 2026
- Doi Number: 10.1142/s0218348x26500726
- Journal Name: Fractals
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
- Keywords: G-calculus, Hermite–Hadamard Inequality, Multiplicative Hadamard Fractional Operators, Multiplicative Katugampola Fractional Operators, Multiplicative Riemann–Liouville Fractional Operators
- Istanbul Gelisim University Affiliated: Yes
Abstract
This paper explores the extension of classical fractional operators to the framework of G-calculus, a non-Newtonian calculus in which differentiation and integration are defined via multiplicative analogs of their classical counterparts. We begin by recalling key concepts from both fractional calculus and G-calculus. Next, we revisit the recently introduced multiplicative Riemann–Liouville fractional operators and extend the multiplicative Riemann–Liouville fractional derivative to arbitrary order α > 0. Building on this foundation, we introduce multiplicative versions of the Hadamard and Katugampola fractional integrals and derivatives. Finally, we establish Hermite–Hadamard inequalities for both newly defined integrals.