Delayed Fractional Discrete Sine and Cosine Matrix Functions and Their Applications to Linear Fractional Delayed Difference Oscillating Systems

Abstract

The fractional discrete retarded cosine and sine matrix functions are defined for the first time in the current paper, and some of their relations are discussed. The variation of constants technique is exploited to obtain an exact analytical form of a general solution to the Cauchy type problem for the linear Riemann-Liouville fractional discrete retarded difference system of order 1 < 2 alpha <= 2 with the noncommutative coefficient matrices. Novel special cases are theoretically presented. In addition, numerical and simulated examples are given to illustrate all of the obtained results.