Abstract
The main aim of this paper is to define a new family of special matrix functions, say, p-Hypergeometric, p-Bessel, p-modified Bessel and p-Tricomi matrix functions, where p is a positive integer. The convergence properties of the p-Hypergeometric matrix function are established and the matrix differential equation is constructed. The differential properties, integral representations, integrals and various particular cases on the p-Bessel matrix function have been obtained. The p-modified Bessel matrix functions, and some properties of this function are investigated. Finally, the p-Tricomi matrix function and several results of the function are defined and studied.