Explicit Solution to the Neutral Fractional and Ordinary Difference Delayed Systems with Noncommutative Coefficient Matrices

Abstract

This paper introduces novel formulations of neutral fractional and ordinary difference delayed systems involving noncommutative coefficient matrices. The corresponding determining neutral matrix equations are established, and an explicit solution is derived through the construction of a neutral discrete delayed matrix exponential based on these equations. A couple of examples with simulations are provided to verify the theoretical findings and to illustrate the efficiency and applicability of the developed results.