{"docId":10205,"paperId":10205,"url":"https:\/\/cm.episciences.org\/10205","doi":"10.46298\/cm.10205","journalName":"Communications in Mathematics","issn":"1804-1388","eissn":"2336-1298","volume":[{"vid":673,"name":"Volume 31 (2023), Issue 1"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"2210.12354","repositoryVersion":2,"repositoryLink":"https:\/\/arxiv.org\/abs\/2210.12354v2","dateSubmitted":"2022-10-25 19:18:09","dateAccepted":"2022-10-25 19:37:53","datePublished":"2022-11-04 13:21:24","titles":["On the matrix function $_pR_q(A, B; z)$ and its fractional calculus properties"],"authors":["Dwivedi, Ravi","Sanjhira, Reshma"],"abstracts":["The main objective of the present paper is to introduce and study the function $_pR_q(A, B; z)$ with matrix parameters and investigate the convergence of this matrix function. The contiguous matrix function relations, differential formulas and the integral representation for the matrix function $_pR_q(A, B; z)$ are derived. Certain properties of the matrix function $_pR_q(A, B; z)$ have also been studied from fractional calculus point of view. Finally, we emphasize on the special cases namely the generalized matrix $M$-series, the Mittag-Leffler matrix function and its generalizations and some matrix polynomials."],"keywords":["Mathematics - Classical Analysis and ODEs"]}