On Hardy-Hilbert-type inequalities with $ \alpha $-fractional derivatives

Marwa M. Ahmed; Wael S. Hassanein; Marwa Sh. Elsayed; Dumitru Baleanu; Ahmed A. El-Deeb; Marwa M. Ahmed; Wael S. Hassanein; Marwa Sh. Elsayed; Dumitru Baleanu; Ahmed A. El-Deeb

doi:10.3934/math.20231126

AIMS Mathematics

2023, Volume 8, Issue 9: 22097-22111. doi: 10.3934/math.20231126

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On Hardy-Hilbert-type inequalities with $ \alpha $-fractional derivatives

1.
Department of Electrical and Computer Engineering, Faculty of Engineering-Girls Campus, King Abdulaziz University, Jeddah, Saudi Arabia
2.
Department of industrial Engineering Faculty of Engineering King Abdulaziz University, Jeddah, Saudi Arabia
3.
Institute of Culture and Science, 6th October City, Cairo 13759, Egypt
4.
Institute of Space Science, Magurele-Bucharest, Romania
5.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
6.
Department of Medical Research, China Medical University, 40402, Taiwan
7.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

Received: 24 April 2023 Revised: 05 June 2023 Accepted: 12 June 2023 Published: 12 July 2023
MSC : 26D10, 26D15, 26D20, 34A12, 34A40

In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Hölder's inequality on time scales and a few algebraic inequalities.
- Steffensen's inequality,
- dynamic inequality,
- dynamic integral,
- time scale
Citation: Marwa M. Ahmed, Wael S. Hassanein, Marwa Sh. Elsayed, Dumitru Baleanu, Ahmed A. El-Deeb. On Hardy-Hilbert-type inequalities with $ \alpha $-fractional derivatives[J]. AIMS Mathematics, 2023, 8(9): 22097-22111. doi: 10.3934/math.20231126

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Abstract

In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Hölder's inequality on time scales and a few algebraic inequalities.

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