Investigation for the k-analogue of τ-Gauss hypergeometric matrix functions and associated fractional calculus.

In this manuscript, we present a new definition of $ (k,\tau) $ (k , τ) -Gauss hypergeometric matrix function and study its analytical properties, like derivative formulas and integral representations. Furthermore, as an application we establish $ {\rm k} $ k -fractional calculus operators for the novel matrix function. We also give some new and known results as special cases of our proposed generalization of the Wright hypergeometric matrix function. [ABSTRACT FROM AUTHOR]