Generalized Hermite-Hadamard and Ostrowski inequalities involving tempered fractional integrals

LAKHDARI A., Abdeljawad T., Alqudah M. A., Mlaiki N.

AIMS Mathematics, cilt.11, sa.3, ss.8467-8491, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.3934/math.2026348
  • Dergi Adı: AIMS Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.8467-8491
  • Anahtar Kelimeler: Hermite-Hadamard inequality, Ostrowski’s inequality, s-convex functions, tempered fractional integrals
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this work, we explored the use of tempered fractional integrals in the development of novel inequalities for differentiable functions that satisfy the s-convexity condition. Drawing upon developments in fractional calculus, we extended several classical results to this generalized setting. We first derived a new version of the Hermite-Hadamard inequality tailored to tempered fractional integrals. Subsequently, we introduced a new integral identity, which serves as a fundamental tool for deriving Ostrowski-type inequalities within the same framework. These contributions enhance the theoretical understanding of fractional calculus and highlight its relevance in modern mathematical analysis. A selection of examples and corollaries is also presented to illustrate the applicability and impact of the proposed results.