A comprehensive analysis of Riemann-Liouville fractional multiplicative integral inequalities

Mhamed Eddahbi; Abdelghani Lakhdari; Badreddine Meftah; Lassaad Mchiri; Mohamed Rhaima; Mhamed Eddahbi; Abdelghani Lakhdari; Badreddine Meftah; Lassaad Mchiri; Mohamed Rhaima

doi:10.3934/math.20251117

AIMS Mathematics

2025, Volume 10, Issue 11: 25227-25252. doi: 10.3934/math.20251117

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Research article

A comprehensive analysis of Riemann-Liouville fractional multiplicative integral inequalities

1.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Z.C. 11451, Riyadh, Saudi Arabia
2.
Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, Türkiye
3.
Department CPST, National Higher School of Technology and Engineering, Annaba 23005, Algeria
4.
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
5.
Panthéon-Assas University Paris Ⅱ, 92 Rue d'Assas, 75006 Paris, France
6.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 02 July 2025 Revised: 05 October 2025 Accepted: 22 October 2025 Published: 04 November 2025
MSC : 26A51, 26D10, 26D15

In this article, we explored a comprehensive class of quadrature formulas characterized by a bi-parametric expression via the concept of multiplicative $ (s, P) $-convexity. Inspired by prior works in this field, we investigated formulas with varying points (ranging from $ 1 $ to $ 4 $) and established associated fractional multiplicative inequalities for functions whose multiplicative first-order derivatives exhibit multiplicative $ (s, P) $-convexity.
- multiplicative calculus,
- Newton-Cotes-type inequalities,
- multiplicative $ (s, P) $-convex functions,
- fractional calculus
Citation: Mhamed Eddahbi, Abdelghani Lakhdari, Badreddine Meftah, Lassaad Mchiri, Mohamed Rhaima. A comprehensive analysis of Riemann-Liouville fractional multiplicative integral inequalities[J]. AIMS Mathematics, 2025, 10(11): 25227-25252. doi: 10.3934/math.20251117

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Abstract

In this article, we explored a comprehensive class of quadrature formulas characterized by a bi-parametric expression via the concept of multiplicative $ (s, P) $-convexity. Inspired by prior works in this field, we investigated formulas with varying points (ranging from $ 1 $ to $ 4 $) and established associated fractional multiplicative inequalities for functions whose multiplicative first-order derivatives exhibit multiplicative $ (s, P) $-convexity.

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