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Research Article | Open Access

Some fractional integral type inequalities for differentiable convex functions

Rabah Debbar1, Abdelkader Moumen2( ), Hamid Boulares3, Badreddine Meftah3, Mohamed Bouye4
Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia
Laboratory of Analysis and Control of Differential Equations "ACED", Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
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Abstract

In this paper, we propose to establish some fractional parametrized three-point integral inequalities. We start by developing a new integral identity. Based on this identity, we derive many types of integral inequality, including Ostrowski, midpoint, trapeze, Simpson, and Bullen. A number of known results are also derived. The findings' applications are given.

Keywords

fractional parametrizedthree-point integral inequalitiesOstrowskimidpointtrapezeSimpsonBullen
CLC number: 26A51, 26D10, 26D15

References

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AIMS Mathematics
Volume 10 Issue 5,
May 2025
Pages 11899-11917
DOI: 10.3934/math.2025537

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Cite this article:
Debbar R, Moumen A, Boulares H, et al. Some fractional integral type inequalities for differentiable convex functions. AIMS Mathematics, 2025, 10(5): 11899-11917. https://doi.org/10.3934/math.2025537

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Received: 01 April 2025
Revised: 01 May 2025
Accepted: 09 May 2025
Published: 15 May 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)