{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T07:05:30Z","timestamp":1760598330566,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we demonstrate that neutral fractional evolution equations with finite delay possess a stable mild solution. Our model incorporates a mixed fractional derivative that combines the Riemann\u2013Liouville and Caputo fractional derivatives with orders 0&lt;\u03b1&lt;1 and 1&lt;\u03b2&lt;2. We identify the infinitesimal generator of the cosine family and analyze the stability of the mild solution using both Hyers\u2013Ulam\u2013Rassias and Hyers\u2013Ulam stability methodologies, ensuring robust and reliable results for fractional dynamic systems with delay. In order to guarantee that the features of invariance under transformations, such as rotations or reflections, result in the presence of fixed points that remain unchanging and represent the consistency and balance of the underlying system, fixed-point theorems employ the symmetry idea. Lastly, the results obtained are applied to a fractional order nonlinear wave equation with finite delay with respect to time.<\/jats:p>","DOI":"10.3390\/sym17010083","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T05:06:34Z","timestamp":1736226394000},"page":"83","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hyers\u2013Ulam and Hyers\u2013Ulam\u2013Rassias Stability for a Class of Fractional Evolution Differential Equations with Neutral Time Delay"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2591-5341","authenticated-orcid":false,"given":"Kholoud N.","family":"Alharbi","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, M., Lv, T., and Wang, Q. 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