Fractional Orders of the Generalized Bessel Matrix Polynomials

M. Abdalla, M. M. Haidan

Abstract

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.

Keywords

Fractional calculus; Generalized Bessel matrix polynomials; Rodrigues’ formula.

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