Rahman Gauhar, Samraiz Muhammad, Shah Kamal, Abdeljawad Thabet, Elmasry Yasser
Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan.
Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan.
Heliyon. 2025 Jan 2;11(1):e41525. doi: 10.1016/j.heliyon.2024.e41525. eCollection 2025 Jan 15.
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 . 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.
由于在数学科学中具有迷人的性质，凸性和分数阶积分算子密切相关。在本文中，我们首先为修正的阿坦加纳 - 巴莱亚努（MAB）分数阶积分算子建立一个恒等式。利用这个恒等式，我们接着应用詹森积分不等式、杨氏不等式、幂平均不等式和赫尔德不等式，来证明关于凸性的奥斯特罗夫斯基型不等式的几个新的推广。从主要发现中，我们还推导出了一些新的特殊情况。预计这项研究的结果将表明分数阶积分不等式研究的新进展。
