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Research Article | Open Access

On some dynamic inequalities of Hilbert's-type on time scales

Ahmed A. El-Deeb1,†( ), Dumitru Baleanu2,3, Nehad Ali Shah4,†, Ahmed Abdeldaim5
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
Institute of Space Science, Magurele-Bucharest, Romania
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt

† These two authors contributed equally to this work and are co-first authors.

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Abstract

In this article, we will prove some new conformable fractional Hilbert-type dynamic inequalities on time scales. These inequalities 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 some algebraic inequalities, conformable fractional Hölder inequalities, and conformable fractional Jensen's inequalities on time scales.

Keywords

Hilbert's inequalitydynamic inequalitytime scales
CLC number: 26D10, 26D15, 26E70, 34A40

References

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 3378-3402
DOI: 10.3934/math.2023174

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Cite this article:
El-Deeb AA, Baleanu D, Shah NA, et al. On some dynamic inequalities of Hilbert's-type on time scales. AIMS Mathematics, 2023, 8(2): 3378-3402. https://doi.org/10.3934/math.2023174

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Received: 12 April 2022
Revised: 02 September 2022
Accepted: 08 October 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)