On the matrix versions of the k analog of ℑ-incomplete Gauss hypergeometric functions and associated fractional calculus

Abstract

In this paper, our aim is to introduce a new definition of ( $k,\Im )$-incomplete Wright hypergeometric matrix functions ( $\left(k,\Im \right)$-IWHMFs) using the $k$-incomplete Pochhammer matrix symbol. First, we define the $k$-incomplete gamma matrix function and introduce the $k$-incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these $\left(k,\Im \right)$-IWHMFs. We have also obtained some results regarding the $k$-fractional calculus operators of these $\left(k,\Im \right)$-IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the $\left(k,\Im \right)$-IWHMFs.