On the matrix function ${}_p{R}_q(A,B;z)$ and its fractional calculus properties

The main objective of the present paper is to introduce and study the function ${}_p{R}_q(A,B;z)$ 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 ${}_p{R}_q(A,B;z)$ are derived. Certain properties of the matrix function ${}_p{R}_q(A,B;z)$ 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.