Extended fractional hermite-hadamard type integral inequalities for h-convex functions with 2D and 3D graphical illustrations

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...

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Vydané v:	Ain Shams Engineering Journal Ročník 17; číslo 1
Hlavní autori:	Abbas, Akhtar, Fiyaz, Fazila, Mubeen, Shahid, Begum Jeelani, Mdi, Alhamzi, Ghaliah
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.01.2026
Predmet:	[formula omitted]- convex functions Fractional integrals Hermite-hadamard inequalities h- convex functions 26A51 Hermite-hadamard inequalities Fractional integrals 26D15 26A33
ISSN:	2090-4479
On-line prístup:	Získať plný text
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Popis
Shrnutí:	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.
ISSN:	2090-4479
DOI:	10.1016/j.asej.2025.103819