Analytical Properties of the Generalized Heat Matrix Polynomials Associated with Fractional Calculus

Abstract

In this paper, we introduce a matrix version of the generalized heat polynomials. Some analytic properties of the generalized heat matrix polynomials are obtained including generating matrix functions, finite sums, and Laplace integral transforms. In addition, further properties are investigated using fractional calculus operators.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

“…In the past few decades, the orthogonal matrix polynomials have attracted a lot of research interest due to their close relations and various applications in many areas of mathematics, engineering, probability theory, graph theory, and physics; for example, see [1][2][3][4][5][6][7][8][9]. In [4], extensions to the matrix framework of the classical families of Legendre, Laguerre, Jacobi, Chebyshev, Gegenbauer, and Hermite polynomials have been introduced.…”