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

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 $\left|\aleph \right|$ . 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.