{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:26:28Z","timestamp":1760149588597,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T00:00:00Z","timestamp":1692921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we derive some classical and fractional properties of the rRs matrix function by using the Hilfer fractional operator. The theory of special matrix functions is the theory of those matrices that correspond to special matrix functions such as the gamma, beta, and Gauss hypergeometric matrix functions. We will also show the relationship with other generalized special matrix functions in the context of the Konhauser and Laguerre matrix polynomials.<\/jats:p>","DOI":"10.3390\/axioms12090817","type":"journal-article","created":{"date-parts":[[2023,8,25]],"date-time":"2023-08-25T08:42:20Z","timestamp":1692952940000},"page":"817","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Relations on the rRs(P,Q,z) Matrix Function"],"prefix":"10.3390","volume":"12","author":[{"given":"Ayman","family":"Shehata","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ghazi S.","family":"Khammash","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Al-Aqsa University-Gaza, Gaza Strip 79779, Palestine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[{"name":"Engineering School, DEIM, Largo dell\u2019Universita, Tuscia University, 01100 Viterbo, Italy"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, Hajibeyli Str., Baku AZ1007, Azerbaijan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/0047-259X(72)90020-6","article-title":"Partial differential equations for hypergeometric functions of two argument matrices","volume":"3","author":"Constantine","year":"1972","journal-title":"J. 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