A variety of dynamic $ \alpha $-conformable Steffensen-type inequality on a time scale measure space

Ahmed A. El-Deeb; Osama Moaaz; Dumitru Baleanu; Sameh S. Askar; Ahmed A. El-Deeb; Osama Moaaz; Dumitru Baleanu; Sameh S. Askar

doi:10.3934/math.2022635

AIMS Mathematics

2022, Volume 7, Issue 6: 11382-11398. doi: 10.3934/math.2022635

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A variety of dynamic $ \alpha $-conformable Steffensen-type inequality on a time scale measure space

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
2.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
3.
Institute of Space Science, Magurele-Bucharest, Romania
4.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
6.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 01 December 2021 Revised: 06 January 2022 Accepted: 16 January 2022 Published: 12 April 2022
MSC : 26D20, 26D10, 34A12, 26D15, 34A40

The main objective of this work is to establish several new alpha-conformable of Steffensen-type inequalities on time scales. Our results will be proved by using time scales calculus technique. We get several well-known inequalities due to Steffensen, if we take $ \alpha = 1 $. Some cases we get continuous inequalities when $ \mathbb{T} = \mathbb{R} $ and discrete inequalities when $ \mathbb{T} = \mathbb{Z} $.
- time scales calculus,
- inequality of Steffensen-type,
- conformable fractional
Citation: Ahmed A. El-Deeb, Osama Moaaz, Dumitru Baleanu, Sameh S. Askar. A variety of dynamic $ \alpha $-conformable Steffensen-type inequality on a time scale measure space[J]. AIMS Mathematics, 2022, 7(6): 11382-11398. doi: 10.3934/math.2022635

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Abstract

The main objective of this work is to establish several new alpha-conformable of Steffensen-type inequalities on time scales. Our results will be proved by using time scales calculus technique. We get several well-known inequalities due to Steffensen, if we take $ \alpha = 1 $. Some cases we get continuous inequalities when $ \mathbb{T} = \mathbb{R} $ and discrete inequalities when $ \mathbb{T} = \mathbb{Z} $.

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