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<p>This paper focuses on the representation of solutions and Hyers-Ulam stability of a linear matrix differential equation with single delay, removing the restriction of matrix commutativity. Firstly, by using the Kronecker product and vectorization methods, we derive the representation of solutions for a homogeneous and nonhomogeneous linear matrix differential equation with single delay. Then, the solution is used to investigate the Hyers-Ulam stability of the related nonhomogeneous equation. Finally, two examples are given to illustrate the main results.</p>

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Representation of Solutions and Hyers-Ulam Stability to a Linear Matrix Differential Equation with Single Delay

  • 期刊论文

  • 发表日期：

    2026年1月2日

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  • Teng Fu,
  • JinRong Wang

摘要

This paper focuses on the representation of solutions and Hyers-Ulam stability of a linear matrix differential equation with single delay, removing the restriction of matrix commutativity. Firstly, by using the Kronecker product and vectorization methods, we derive the representation of solutions for a homogeneous and nonhomogeneous linear matrix differential equation with single delay. Then, the solution is used to investigate the Hyers-Ulam stability of the related nonhomogeneous equation. Finally, two examples are given to illustrate the main results.