{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:47:50Z","timestamp":1760230070395,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T00:00:00Z","timestamp":1657497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, by using some algebraic inequalities, nabla H\u00f6lder inequalities, and nabla Jensen\u2019s inequalities on timescales, we proved some new nabla Hilbert-type dynamic inequalities on timescales. These inequalities extend some known dynamic inequalities on timescales and unify some continuous inequalities and their corresponding discrete analogues. Symmetry plays an essential role in determining the correct methods to solve dynamic inequalities.<\/jats:p>","DOI":"10.3390\/sym14071421","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T03:50:36Z","timestamp":1657597836000},"page":"1421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Some Important Dynamic Inequalities of Hardy\u2013Hilbert-Type on Timescales"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2822-4092","authenticated-orcid":false,"given":"Ahmed A.","family":"El-Deeb","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Institute of Space Science, 077125 Magurele, Romania"},{"name":"Department of Mathematics, Cankaya University, Ankara 06530, Turkey"},{"name":"Department of Medical Research, China Medical University, Taichung 40447, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1824-4065","authenticated-orcid":false,"given":"Ahmed","family":"Abdeldaim","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42511, Egypt"},{"name":"Faculty of Science and Humanities, Shaqra University, P.O. Box 18, Al-Dawadmi 11911, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,11]]},"reference":[{"unstructured":"Hardy, G.H., Littlewood, J.E., and P\u00f3lya, G. (1952). Inequalities, Cambridge University Press. MR 13,727e. Zbl 634.26008.","key":"ref_1"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"293","DOI":"10.5556\/j.tkjm.29.1998.4258","article-title":"A note on Hilbert-type inequality","volume":"29","author":"Pachpatte","year":"1998","journal-title":"Tamkang J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"311","DOI":"10.5556\/j.tkjm.31.2000.389","article-title":"A Hilbert-type inequality","volume":"31","author":"Handley","year":"1998","journal-title":"Tamkang J. 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Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser.","key":"ref_11","DOI":"10.1007\/978-1-4612-0201-1"},{"doi-asserted-by":"crossref","unstructured":"El-Deeb, A.A., Makharesh, S.D., Askar, S.S., and Awrejcewicz, J. (2022). A variety of Nabla Hardy\u2019s type inequality on time scales. Mathematics, 10.","key":"ref_12","DOI":"10.3390\/math10050722"},{"doi-asserted-by":"crossref","unstructured":"El-Deeb, A.A., and Baleanu, D. (2022). Some new dynamic Gronwall-Bellman-Pachpatte type inequalities with delay on time scales and certain applications. J. Inequal. 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