Analytical Solutions and Hyers–Ulam Stability Criteria for Sylvester-Type Fractional Matrix Delay Systems

The explicit solution formulation and Hyers–Ulam Stability of Sylvester-type fractional delay differential matrix equations are considered. The analysis begins with the derivation of explicit solution representations, facilitated by a novel class of delayed Mittag-Leffler-type matrix functions. Subsequently, these representations are leveraged to establish sufficient conditions for Hyers–Ulam stability, supported by norm estimations of the newly defined matrix functions. The validity and effectiveness of the theoretical results are demonstrated by means of a numerical example.