Bennett-Leindler nabla type inequalities via conformable fractional derivatives on time scales

Ahmed A. El-Deeb; Samer D. Makharesh; Sameh S. Askar; Dumitru Baleanu; Ahmed A. El-Deeb; Samer D. Makharesh; Sameh S. Askar; Dumitru Baleanu

doi:10.3934/math.2022777

AIMS Mathematics

2022, Volume 7, Issue 8: 14099-14116. doi: 10.3934/math.2022777

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Bennett-Leindler nabla type inequalities via conformable fractional derivatives on time scales

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
2.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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

Received: 06 January 2022 Revised: 27 March 2022 Accepted: 07 April 2022 Published: 27 May 2022
MSC : 26D10, 26D15, 34N05, 26E70

In this work, we prove several new $ (\gamma, a) $-nabla Bennett and Leindler dynamic inequalities on time scales. The results proved here generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using integration by parts, chain rule and Hölder inequality for the $ (\gamma, a) $-nabla-fractional derivative on time scales.
- Steffensen's inequality,
- dynamic inequality,
- dynamic integral,
- time scales
Citation: Ahmed A. El-Deeb, Samer D. Makharesh, Sameh S. Askar, Dumitru Baleanu. Bennett-Leindler nabla type inequalities via conformable fractional derivatives on time scales[J]. AIMS Mathematics, 2022, 7(8): 14099-14116. doi: 10.3934/math.2022777

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Abstract

In this work, we prove several new $ (\gamma, a) $-nabla Bennett and Leindler dynamic inequalities on time scales. The results proved here generalize some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using integration by parts, chain rule and Hölder inequality for the $ (\gamma, a) $-nabla-fractional derivative on time scales.

References

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