Visualizing Some Fractional Ostrowski-Type Integral Inequalities Through 2D and 3D Graphs
Abstract
In this paper, we extend Ostrowski-type integral inequalities using the generalized Atangana–Baleanu fractional integral operator. We derive an extended form of Ostrowski-type integral inequalities by incorporating the power-mean inequality, Hölder's inequality, Young's inequality, and Jensen's integral inequality under convexity conditions. The results are supported by numerical examples and graphical illustrations, including both 2D and 3D representations. These visual insights enhance the understanding of the analytical results and highlight the sharpness and applicability of the derived inequalities. Additionally, we explore special cases and compare our findings with existing inequalities to demonstrate the significance of the proposed extensions. The presented results contribute to the ongoing development of fractional calculus and provide new perspectives for further research in fractional integral inequalities.
Keywords
Atangana-Baleanu fractional integral operator, Ostrowski integral inequalities, Convex functions, H\"older inequality, Power mean inequality, Young's inequality
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