Advancements in Integral Inequalities Through Hattaf Fractional Operators (Contemporary Mathematics, 2025)
In studies of inequality theory, integral identities are developed to support numerous inequalities. Various fractional integral and derivative operators have been employed recently to accomplish these identities. In this article, we first establish an integral identity by employing Hattaf fractional integral operators. Then, we use this identity to give some novel generalizations of integral inequalities for the convexity of |ℵ| using the Jensen integral inequality, Young's inequality, power-mean inequality, and Hölder inequality. The main motivating goal of this study is to use Hattaf-fractional integral operators with strong kernel structure to derive new and general form of integral inequalities.
Keywords: young inequality; convex function; power-mean inequality; fractional operators