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Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations and differential formulae concerning it. We also present the Mellin matrix transform of the extended Wright hypergeometric matrix function. After that, we present some fractional calculus findings for these expanded Wright hypergeometric matrix functions. Lastly, we present several theorems of the extended Wright hypergeometric matrix function in fractional Kinetic equations. [ABSTRACT FROM AUTHOR]

In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function. [ABSTRACT FROM AUTHOR]