New techniques for solving some matrix and matrix differential equations

Matrix and matrix differential equations play an important role in system theory, control theory, stability theory of differential equations, communication systems and many other fields. In this paper, we present the solutions of non-homogeneous matrix differential equations, convolution matrix differential equations and matrix equations which include the renewal matrix equation by using convolution and Kronecker products of matrices. Furthermore, the existence and uniqueness of the solution of some important and interesting special cases of these equations are also considered with some illustrated examples in order to show our new approaches.