Research Information System
Journal of Computational and Applied Mathematics, vol.486, 2026 (SCI-Expanded, Scopus)
This work presents explicit solution representations for first- and second-order linear matrix differential equations subject to a single pure delay, formulated without the simplifying assumption of commutativity either among the coefficient matrices or with the inhomogeneous term. The analysis relies on generalized binomial constructions together with delayed exponential, sine, and cosine matrix functions, through which we establish a unified and systematic framework for constructing fundamental solutions in noncommutative settings. Additionally, the stability properties of the system, including Ulam Hyers stability, are analyzed within this framework, demonstrating how the delay and noncommutative structure influence the stability and robustness of the solutions. The approach is illustrated by representative examples that highlight both the practical applicability of the method and the significant effects that delay and noncommutativity exert on the qualitative behavior of the system dynamics. Importantly, the obtained results are not only novel in the context of delayed systems but also yield new contributions to the theory of nondelayed matrix differential equations.