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

Abstract

In this manuscript, we present a new definition of $(k,\tau )$-Gauss hypergeometric matrix function and study its analytical properties, like derivative formulas and integral representations. Furthermore, as an application we establish $\mathrm{k}$-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.

Keywords:

• Generalized $\tau -$Gauss matrix function
• derivative formulas
• integral representations
• k-Fractional calculus

2020 Mathematics subject classifications:

• 15A15
• 33C05
• 33E20
• 34A05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

No data were used to support the study.

Additional information

Funding

The third author extends their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Larg Groups [grant number R.G.P.2/144/43].