On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus

Abstract

Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol. First, we give a generalization of the extended incomplete Wright hypergeometric matrix function and state some integral equations and differential formulas about it. Next, we obtain some results about fractional calculus of these extended incomplete Wright hypergeometric matrix functions. Finally, we discuss an application of the extended incomplete Wright hypergeometric matrix function in the kinetic equations.

On the extended Wright hypergeometric matrix function and its properties

“…In this section, motivated by [21], we introduce the incomplete extended Wright hypergeometric matrix function (IEWHMF) with the help of the incomplete extended beta matrix function defined in (8). Let B, C and X be positive stable matrices in C r×r satisfying the condition (2), and suppose B, C and X commute with each other.…”

“…Furthermore, the incomplete Wright hypergeometric matrix function was defined and some of its properties were established. We remark in passing that the incomplete extension of the Pochhammer matrix symbol, which was also considered by Bakhet et al [9], has also been used rather widely in the current literature on hypergeometric functions (see, for example, [2], [8], [18] and [19], and references therein). On the other hand, very recently, the authors (see [1,3,11] ) introduced the extensions of the (k; τ )-Gauss hypergeometric matrix function and obtained their various properties.…”