{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T14:06:14Z","timestamp":1773151574289,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work presents new results concerning weighted Hardy-type inequalities within the framework of delta conformable fractional integrals on arbitrary time scales. The proposed approach unifies the treatment of inequalities across continuous and discrete domains, enabling the derivation of original forms in both settings. The obtained results exhibit symmetry with classical inequalities, and several integral and discrete inequalities arise as special cases. These findings extend and generalize known results and enrich the theory of integral inequalities in fractional and dynamic calculus, providing a versatile platform for further developments in symmetric and weighted inequality analysis.<\/jats:p>","DOI":"10.3390\/sym17091573","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T16:53:42Z","timestamp":1758300822000},"page":"1573","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Novel Weighted Dynamic Hardy-Type Inequalities in the Framework of Delta Conformable Calculus on Time Scales"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6782-7908","authenticated-orcid":false,"given":"Haytham M.","family":"Rezk","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed R.","family":"El-Saeed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Mousa","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Future University in Egypt, Cairo 11835, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7929-2901","authenticated-orcid":false,"given":"Karim A.","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Faculty of Engineering Technology, ElSewedy University of Technology, Cairo 44916, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,19]]},"reference":[{"key":"ref_1","first-page":"150","article-title":"Notes on some points in the integral calculus (LX)","volume":"54","author":"Hardy","year":"1925","journal-title":"Mess. 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