Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems

In this paper we consider Bessel equations of the type ${\displaystyle t^2{X}^{\left(2\right)}\left(t\right)+t{X}^{\left(1\right)}\left(t\right)+(t^{2}I-A^2)X\left(t\right)=0}$, where A is an n${\displaystyle \times }$n complex matrix and X(t) is an n${\displaystyle \times }$m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.