Hermite-Hadamard type inequalities for Co-ordinated convex functions with variable-order fractional integrals
APPLIED AND COMPUTATIONAL MATHEMATICS, vol.24, no.2, pp.326-343, 2025 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 24 Issue: 2
- Publication Date: 2025
- Doi Number: 10.30546/1683-6154.24.2.2025.326
- Journal Name: APPLIED AND COMPUTATIONAL MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.326-343
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
Abstract
This study develops a novel framework for Hermite-Hadamard-type inequalities by employing multivariate variable-order Riemann-Liouville fractional integral operators. These operators, which extend classical fractional calculus, allow fractional orders to vary dynamically, providing a powerful tool for capturing spatially and temporally dependent behaviors in multidimensional systems. We rigorously define the variable-order fractional integrals with new formulations of lower and upper bounds tailored for Hermite-Hadamard-type inequalities. By analyzing the properties and well-posedness of the proposed operators, we establish generalized Hermite-Hadamard inequalities for coordinated convex functions. These results represent a significant advancement in fractional analysis, bridging the gap between classical results and the more flexible, dynamic nature of variable-order systems. This work lays the foundation for further exploration of fractional inequalities and their application in systems governed by varying memory effects.