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

Ahmed A. El-Deeb; Dumitru Baleanu; Nehad Ali Shah; Ahmed Abdeldaim; Ahmed A. El-Deeb; Dumitru Baleanu; Nehad Ali Shah; Ahmed Abdeldaim

doi:10.3934/math.2023174

AIMS Mathematics

2023, Volume 8, Issue 2: 3378-3402. doi: 10.3934/math.2023174

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

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
2.
Institute of Space Science, Magurele-Bucharest, Romania
3.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
4.
Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea
5.
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.

Received: 12 April 2022 Revised: 02 September 2022 Accepted: 08 October 2022 Published: 18 November 2022
MSC : 26D10, 26D15, 26E70, 34A40

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.
- Hilbert's inequality,
- dynamic inequality,
- time scales
Citation: Ahmed A. El-Deeb, Dumitru Baleanu, Nehad Ali Shah, Ahmed Abdeldaim. On some dynamic inequalities of Hilbert's-type on time scales[J]. AIMS Mathematics, 2023, 8(2): 3378-3402. doi: 10.3934/math.2023174

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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.

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