(untitled) (European Journal of Pure and Applied Mathematics, 2017)
This paper presents and investigates generalized Bessel matrix polynomials (GBMPs) with order ∈ 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(t;A; B); t ∈ C, for matrices A and B in the complex space CNN 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.