Advancements in integral inequalities of Ostrowski type via modified Atangana-Baleanu fractional integral operator

Gauhar Rahman; Muhammad Samraiz; Kamal Shah; Thabet Abdeljawad; Yasser Elmasry

doi:10.1016/j.heliyon.2024.e41525

Advancements in integral inequalities of Ostrowski type via modified Atangana-Baleanu fractional integral operator

Heliyon. 2025 Jan 2;11(1):e41525. doi: 10.1016/j.heliyon.2024.e41525. eCollection 2025 Jan 15.

Authors

Gauhar Rahman¹, Muhammad Samraiz², Kamal Shah³, Thabet Abdeljawad^{4

3

5

6

7}, Yasser Elmasry⁸

Affiliations

¹ Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan.
² Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan.
³ Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
⁴ Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India.
⁵ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.
⁶ Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa.
⁷ Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally, 32093, Kuwait.
⁸ Department of Mathematics, College of Science - King Khalid University, P.O. Box 9004, Abha 61466, Saudi Arabia.

Abstract

Convexity and fractional integral operators are closely related due to their fascinating properties in the mathematical sciences. In this article, we first establish an identity for the modified Atangana-Baleanu (MAB) fractional integral operators. Using this identity, we then apply Jensen integral inequality, Young's inequality, power-mean inequality, and Hölder inequality to prove several new generalizations of Ostrowski type inequality for the convexity of $| ℵ |$ . From the primary findings, we also deduced a few new special cases. The results of this investigation are expected to indicate new advances in the study of fractional integral inequalities.

Keywords: 26A33; 26A51; 26D10; Convex function; Fractional operators; Power mean inequality; Young inequality.