Explicit Solution and Ulam–Hyers Stability of the Two-Sided Matrix Caputo Fractional Delay Differential Equations with a Single Time Lag

In this paper, we investigate initial-value problems for two-sided matrix Caputo fractional delay differential equations with a single time lag. Combining the method of steps with the vectorization technique, we derive explicit solution representations for such linear two-sided matrix systems. Furthermore, we analyze the Ulam–Hyers stability of the considered systems. Two illustrative numerical examples are presented to demonstrate our main theoretical findings. Our key results resolve several open problems recently proposed in the literature.