Abstract
This paper presents and investigates generalized Bessel matrix polynomials (GBMPs) with order alpha is an element of R (the set of real numbers). The given result is supposed to be an enhanced and a generalized form of the scalar form to the fractional analysis setting. By using the Liouville-Caputo operator of fractional analysis and Rodrigues type representation form of fractional order, the generalized Bessel matrix functions (GBMFs) Y-alpha(t; A, B), t is an element of C, for matrices A and M in the complex space C-NxN are derived and supplied with a matrix hypergeometric representation that are satisfied by these functions. Subsequently, a fractional matrix recurrence relationship, a fractional matrix of second-order differential equation and an orthogonal system are then developed for GBMFs.