Generalized Hermite-Hadamard and Ostrowski inequalities involving tempered fractional integrals
AIMS Mathematics, vol.11, no.3, pp.8467-8491, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: 3
- Publication Date: 2026
- Doi Number: 10.3934/math.2026348
- Journal Name: AIMS Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
- Page Numbers: pp.8467-8491
- Keywords: Hermite-Hadamard inequality, Ostrowski’s inequality, s-convex functions, tempered fractional integrals
- Istanbul Gelisim University Affiliated: Yes
Abstract
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.