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Hyers–Ulam Stability of Linear Quaternion-Valued Differential Equations with Two-Sided Constant Coefficients

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Abstract

In this paper, the Hyers–Ulam stability of linear quaternion-valued differential equations with two-sided constant coefficients are studied. Utilizing the complex representation of quaternions, we transform a nth-order quaternion-valued differential equation with two-sided constant coefficients into four nth-order complex differential equations. Then we derive the Hyers–Ulam stability by means of the reduced order method and the relationship between the quaternion-valued differential equations and the system of complex-valued differential equations. Two examples are presented to illustrate the validity of the theoretical results.

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Funding

This work is partially supported by the National Natural Science Foundation of China (12161015).

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Jiaojiao Lv, JinRong Wang & Kui Liu

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  1. Jiaojiao Lv
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  2. JinRong Wang
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  3. Kui Liu
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Correspondence to JinRong Wang or Kui Liu.

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Lv, J., Wang, J. & Liu, K. Hyers–Ulam Stability of Linear Quaternion-Valued Differential Equations with Two-Sided Constant Coefficients. Qual. Theory Dyn. Syst. 23, 141 (2024). https://doi.org/10.1007/s12346-024-00997-y

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