Extended fractional hermite-hadamard type integral inequalities for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si20.svg"> <mml:mrow> <mml:mi mathvariant="sans-serif">h</mml:mi> </mml:mrow> </mml:math> -convex functions with <mml

In this paper, we establish new fractional Hermite–Hadamard type inequalities using k-Riemann–Liouville fractional integrals for differentiable h-convex functions. By employing k-Riemann Riouville fractional integrals and differentiable h-convex functions, our results extend and refine the existing inequalities in literature and show the connection between them. We discuss special cases of our derived inequalities which highlight the applicability and novelty of our approach. Furthermore, to support and visualize the theoretical findings, we provide detailed 2D and 3D graphical verifications of the main inequalities. These illustrations offer deeper insights into the behavior of the inequalities and demonstrate their practical relevance. Applications and future research directions are also addressed.