On a generalization of Wright hypergeometric matrix function and their properties

Abstract

Several features of the Wright hypergeometric matrix function $_2 R_1 ^{(\tau)}(L,M;N; z)$ were obtained and published recently by Bakhet et al. \cite{9}. Abdalla \cite{6} has used fractional operators on this function. In this paper, we present a generalized form of the Wright hypergeometric matrix function, $_2R_1 ^{(\tau)}((L;\mathbb{L}),M;N; z;\mathbb{X,Y})$, with the aid of the generalized Pochhammer matrix symbol $(L;M)_n$ and the generalized beta matrix function $\mathcal{B}(A,B;\mathbb{X,Y})$. For this expanded form, we construct a number of potentially helpful conclusions, including fractional derivatives and integral representations. Additionally, we obtain a few characteristics of the associated incomplete extended Wright hypergeometric matrix function.