Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities

Hüseyin Budak; Abd-Allah Hyder; Hüseyin Budak; Abd-Allah Hyder

doi:10.3934/math.20231572

AIMS Mathematics

2023, Volume 8, Issue 12: 30760-30776. doi: 10.3934/math.20231572

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Research article

Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities

Hüseyin Budak ¹,
Abd-Allah Hyder ^{2
,
,}

1.
Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce 81620, Turkey
2.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

Received: 28 August 2023 Revised: 02 November 2023 Accepted: 06 November 2023 Published: 14 November 2023
MSC : 26D07, 26D10, 26D15

In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.
- Milne type inequalities,
- convex function,
- fractional integrals,
- bounded function,
- function of bounded variation
Citation: Hüseyin Budak, Abd-Allah Hyder. Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities[J]. AIMS Mathematics, 2023, 8(12): 30760-30776. doi: 10.3934/math.20231572

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Abstract

In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.

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