EXPLORING CONFORMABLE FRACTIONAL INTEGRAL INEQUALITIES: A MULTI-PARAMETER APPROACH

Abdelghani Lakhdari, Nabil Mlaiki, Wedad Saleh, Thabet Abdeljawad and Badreddine Meftah
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Abdelghani Lakhdari: Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus Kocaeli 41001, Türkiye†Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria
Nabil Mlaiki: ��Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
Wedad Saleh: �Department of Mathematics, Taibah University, Al-Medina 42353, Saudi Arabia
Thabet Abdeljawad: ��Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia¶Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India∥Department of Medical Research, China Medical University, Taichung 40402, Taiwan**Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University Ga-Rankuwa, Medusa 0204, South Africa††Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea§§Centre for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally 32093, Kuwait
Badreddine Meftah: ��‡Laboratory of Analysis and Control of Differential Equations “ACED†, Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-20

Abstract: In this paper, we conduct a comprehensive investigation into conformable fractional integral inequalities, introducing a novel multi-parameter integral identity as a foundational tool for deriving significant results related to the Newton–Cotes formulas for one, two, and three points. These formulas are explored within the contexts of both conformable fractional integrals and Riemann–Liouville fractional integrals. Among the findings, this study provides new results, including refinements of several previously established results, thereby enhancing the existing body of knowledge. Numerical examples and graphical illustrations are provided to demonstrate the accuracy and effectiveness of the derived outcomes. This work offers fresh insights into the role of fractional integrals in numerical analysis, with potential applications across various scientific disciplines.

Keywords: Conformable Fractional Integrals; Riemann–Liouville Fractional Integrals; Multi-parameter Identity; Convex Functions (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500550

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