Fractional Milne-type inequalities for twice differentiable functions

Areej A. Almoneef; Abd-Allah Hyder; Hüseyin Budak; Mohamed A. Barakat; Areej A. Almoneef; Abd-Allah Hyder; Hüseyin Budak; Mohamed A. Barakat

doi:10.3934/math.2024965

AIMS Mathematics

2024, Volume 9, Issue 7: 19771-19785. doi: 10.3934/math.2024965

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Research article

Fractional Milne-type inequalities for twice differentiable functions

1.
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
3.
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkey
4.
Department of Basic Science, University college of Alwajh, University of Tabuk, Saudi Arabia

Received: 10 May 2024 Revised: 31 May 2024 Accepted: 04 June 2024 Published: 17 June 2024
MSC : 26D15, 26D10, 26D07

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.
- Milne-type inequalities,
- fractional integrals,
- convexity,
- differentiable functions
Citation: Areej A. Almoneef, Abd-Allah Hyder, Hüseyin Budak, Mohamed A. Barakat. Fractional Milne-type inequalities for twice differentiable functions[J]. AIMS Mathematics, 2024, 9(7): 19771-19785. doi: 10.3934/math.2024965

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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.

References

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