A novel fractional delayed matrix cosine and sine

Abstract

We introduce the fractional delayed matrix cosine and sine functions and use the variation of constants method to obtain an explicit formula for a solution to the initial value problem for a Riemann-Liouville sequential fractional linear time-delay system of order 1 < 2 alpha <= 2. Our results extend those for fractional linear time-delay systems and novel for the classical case alpha = 1. (C) 2019 Elsevier Ltd. All rights reserved.