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Research Article | Open Access

Fractional Milne-type inequalities for twice differentiable functions

Areej A. Almoneef1( ), Abd-Allah Hyder2, Hüseyin Budak3, Mohamed A. Barakat4
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkey
Department of Basic Science, University college of Alwajh, University of Tabuk, Saudi Arabia
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Abstract

In this study, a specific identity was derived for functions that possess two continuous derivatives. Through the utilization of this identity and Riemann-Liouville fractional integrals, several fractional Milne-type inequalities were established for functions whose second derivatives inside the absolute value are convex. Additionally, an example and a graphical representation are included to clarify the core findings of our research.

Keywords

Milne-type inequalitiesfractional integralsconvexitydifferentiable functions
CLC number: 26D15, 26D10, 26D07

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 19771-19785
DOI: 10.3934/math.2024965

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Cite this article:
Almoneef AA, Hyder A-A, Budak H, et al. Fractional Milne-type inequalities for twice differentiable functions. AIMS Mathematics, 2024, 9(7): 19771-19785. https://doi.org/10.3934/math.2024965

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Received: 10 May 2024
Revised: 31 May 2024
Accepted: 04 June 2024
Published: 15 July 2024
©2024 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)