New fractional Hermite–Hadamard and Fejér inequalities involving special functions with applications to numerical quadrature rules

Haitham Qawaqneh; Waqar Afzal; Mujahid Abbas; Muhammad Tariq; Mehreen Shehzadi Khan; Siegfried Macías; Jorge E. Macías-Díaz; Hijaz Ahmad; Waleed Mohammed Abdelfattah

doi:10.46481/jnsps.2026.3543

Authors

Haitham Qawaqneh
Department of Basic Sciences, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
Waqar Afzal
Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan;

Center for Theoretical Physics, Khazar University, 41 Mehseti Str., Baku AZ1096, Azerbaijan;

International Center for Interdisciplinary Research in Sciences, University of Lahore, Lahore 54792, Pakistan
Mujahid Abbas
Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg 2092, South Africa
Muhammad Tariq
Mathematics Research Center, Near East University, Near East Boulevard, Nicosia, Mersin 99138, Turkey
Mehreen Shehzadi Khan
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
Siegfried Macías
Department of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes 20100, Mexico
Jorge E. Macías-Díaz
Department of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes 20100, Mexico
Hijaz Ahmad
[email protected]

Irfan Suat Günsel Operational Research Institute, Near East University, Nicosia/TRNC, Mersin 10, 99138, Turkey;

Department of Mathematics, College of Science, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, South Korea
Waleed Mohammed Abdelfattah
College of Engineering, University of Business and Technology, Jeddah 23435, Saudi Arabia;

Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, P.O. 44519, Egypt

Keywords:

Gamma and Beta functions, Interval-valued Katugampola fractional integrals, Hermite–Hadamard and Fejér inequalities, Interval-valued convex mappings, Numerical quadrature

Abstract

The principal objective of this article is to establish new and refined variants of Hermite--Hadamard- and Fej'{e}r-type integral inequalities in the interval-valued setting by exploiting the auxiliary transformed mapping mathcal{G}(s) := mathcal{F}(s^{1/rho}). This transformation preserves convexity and facilitates the systematic application of fractional integral techniques over a suitably rescaled domain through the Katugampola fractional operator. The resulting bounds are expressed explicitly in terms of the Gamma function, which enriches the analytical structure of the inequalities and yields sharper and more precise estimates than existing results. The validity and applicability of the theoretical findings are demonstrated through nontrivial illustrative examples and detailed remarks, and several previously known inequalities are recovered as limiting cases under suitable parameter configurations. As a further application, the derived inequalities are used to construct inclusion-type error estimates for numerical quadrature rules, with particular emphasis on the trapezoidal rule applied to interval-valued functions in the Katugampola fractional framework.

Dimensions

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