On the extended Wright hypergeometric matrix function and its properties

Abstract

Recently, Bakhet et al. [9] presented the Wright hypergeometric matrix function $_{2}R_{1}^{(\tau )}(A,B;C;z)$ and derived several properties. Abdalla [6] has since applied fractional operators to this function. In this paper, with the help of the generalized Pochhammer matrix symbol $(A;B)_{n}$ and the generalized beta matrix function $\mathcal{B}(P,Q;\mathbb{X})$, we introduce and study an extended form of the Wright hypergeometric matrix function, $_{2}R_{1}^{(\tau )}((A,\mathbb{A}),B;C;z;\mathbb{X}).$ We establish several potentially useful results for this extended form, such as integral representations and fractional derivatives. We also derive some properties of the corresponding incomplete extended Wright hypergeometric matrix function.