## 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 properties

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.

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