Generalized Hermite-Hadamard and Ostrowski inequalities involving tempered fractional integrals

Abdelghani Lakhdari; Thabet Abdeljawad; Manar A. Alqudah; Nabil Mlaiki; Abdelghani Lakhdari; Thabet Abdeljawad; Manar A. Alqudah; Nabil Mlaiki

doi:10.3934/math.2026348

AIMS Mathematics

2026, Volume 11, Issue 3: 8467-8491. doi: 10.3934/math.2026348

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Generalized Hermite-Hadamard and Ostrowski inequalities involving tempered fractional integrals

1.
Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria
2.
Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Kocaeli, Türkiye
3.
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, Tamil Nadu, India
4.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
5.
Department of Fundamental Sciences, Faculty of Engineering and Architecture, Istanbul Gelisim University, Avcılar-Istanbul, 34310, Türkiye
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, 02447 Seoul, Korea
8.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84424, Riyadh 11671, Saudi Arabia

Received: 20 January 2026 Revised: 05 March 2026 Accepted: 19 March 2026 Published: 30 March 2026
MSC : 25A51, 25D10, 25D15

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.
- Hermite-Hadamard inequality,
- Ostrowski's inequality,
- tempered fractional integrals,
- $ s $-convex functions
Citation: Abdelghani Lakhdari, Thabet Abdeljawad, Manar A. Alqudah, Nabil Mlaiki. Generalized Hermite-Hadamard and Ostrowski inequalities involving tempered fractional integrals[J]. AIMS Mathematics, 2026, 11(3): 8467-8491. doi: 10.3934/math.2026348

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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.

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