On the matrix function $_pR_q(A, B; z)$ and its fractional calculus properties

Ravi Dwivedi; Reshma Sanjhira

doi:10.46298/cm.10205

Ravi Dwivedi ; Reshma Sanjhira - On the matrix function $_pR_q(A, B; z)$ and its fractional calculus properties

cm:10205 - Communications in Mathematics, November 4, 2022, Volume 31 (2023), Issue 1 - https://doi.org/10.46298/cm.10205

On the matrix function $_pR_q(A, B; z)$ and its fractional calculus propertiesArticle

Authors: Ravi Dwivedi ; Reshma Sanjhira

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.

https://doi.org/10.46298/cm.10205

Source: arXiv.org:2210.12354

Volume: Volume 31 (2023), Issue 1

Published on: November 4, 2022

Accepted on: October 25, 2022

Submitted on: October 25, 2022

Keywords: Mathematics - Classical Analysis and ODEs

Licence: Attribution 4.0 International (CC BY 4.0)