Some fractional integral type inequalities for differentiable convex functions

Rabah Debbar; Abdelkader Moumen; Hamid Boulares; Badreddine Meftah; Mohamed Bouye; Rabah Debbar; Abdelkader Moumen; Hamid Boulares; Badreddine Meftah; Mohamed Bouye

doi:10.3934/math.2025537

AIMS Mathematics

2025, Volume 10, Issue 5: 11899-11917. doi: 10.3934/math.2025537

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Research article

Some fractional integral type inequalities for differentiable convex functions

1.
Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria
2.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia
3.
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
4.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

Received: 01 April 2025 Revised: 01 May 2025 Accepted: 09 May 2025 Published: 22 May 2025
MSC : 26A51, 26D10, 26D15

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.
- fractional parametrized,
- three-point integral inequalities,
- Ostrowski,
- midpoint,
- trapeze,
- Simpson,
- Bullen
Citation: Rabah Debbar, Abdelkader Moumen, Hamid Boulares, Badreddine Meftah, Mohamed Bouye. Some fractional integral type inequalities for differentiable convex functions[J]. AIMS Mathematics, 2025, 10(5): 11899-11917. doi: 10.3934/math.2025537

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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.

References

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