Hermite-Hadamard type inequalities for Co-ordinated convex functions with variable-order fractional integrals

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Yalçın A., Gül E., Akdemir A. O.

APPLIED AND COMPUTATIONAL MATHEMATICS, cilt.24, sa.2, ss.326-343, 2025 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.30546/1683-6154.24.2.2025.326
  • Dergi Adı: APPLIED AND COMPUTATIONAL MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.326-343
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.