{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T04:40:32Z","timestamp":1760071232978,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T00:00:00Z","timestamp":1759881600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Research Support Project","award":["PNURSP2025R45"],"award-info":[{"award-number":["PNURSP2025R45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This work investigates a new category of linear non-homogeneous discrete-matrix equations that feature multiple delays and first-order differences, under the assumption of pairwise permutable coefficient matrices. We define a novel multi-delayed discrete-matrix-exponential function that extends previous concepts. Using this function and specific commutativity properties, we construct an explicit matrix solution. The study highlights the advantages of our approach by contrasting it with prior research and identifying new open questions. Finally, a numerical example illustrates the application and relevance of the derived solution.<\/jats:p>","DOI":"10.3390\/sym17101684","type":"journal-article","created":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T12:04:52Z","timestamp":1759925092000},"page":"1684","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exact Solutions to Multiple-Delayed Linear Discrete Matrix Equations"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3574-2939","authenticated-orcid":false,"given":"Ahmed M.","family":"Elshenhab","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2222-7973","authenticated-orcid":false,"given":"Ghada","family":"AlNemer","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7968-7188","authenticated-orcid":false,"given":"Xingtao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Harbin Institute of Technology, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3997","DOI":"10.1002\/mma.9799","article-title":"Representation of solutions and finite-time stability for fractional delay oscillation difference equations","volume":"47","author":"Chen","year":"2024","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"838","DOI":"10.15388\/namc.2025.30.41799","article-title":"Finite-time stability of discrete fractional uncertain recurrent neural networks","volume":"30","author":"Huang","year":"2025","journal-title":"Nonlinear Anal. Model. 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Difference Equations and Inequalities: Theory, Methods, and Applications, Marcel Dekker. [2nd ed.].","DOI":"10.1201\/9781420027020"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1684\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T04:25:45Z","timestamp":1760070345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1684"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,8]]},"references-count":28,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["sym17101684"],"URL":"https:\/\/doi.org\/10.3390\/sym17101684","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,10,8]]}}}