The general (vector) solutions of such linear (coupled) matrix fractional differential equations by using Kronecker structures

Abstract

In this paper, we demonstrate how Kronecker products and vector operator can be combined beautifully to solve and fit the non-homogenous linear matrix fractional differential equations and such coupled linear matrix fractional differential equations. The way exists which transform the given (coupled) matrix fractional differential equations by using Kronecker structures into forms for which solutions may be readily computed. Some important and interesting special cases of the general system of non-homogeneous linear matrix fractional differential equations of fractional order are also considered which includes the non-homogenous linear fractional dynamical system with delays in control. Finally, a brief comparison between the fractional and integer order (vector) solutions and some examples are given to illustrate our new approaches. © 2014 Elsevier Inc. All rights reserved.