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On the Stability of Linear Quaternion-Valued Differential Equations

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Abstract

This paper deals with the stability of linear quaternion-valued differential equations. First, we derive an explicit norm estimation like the matrix exponential function in the sense of quaternion-valued. Second, we use this norm to show that the first-order linear equations are asymptotically stable and Hyers–Ulam’s type stable. Further, we show that nth-order equations are also generalized Hyers–Ulam stability. Some examples which can effectively illustrate the theoretical results are presented.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

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Authors and Affiliations

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

    Dan Chen & JinRong Wang

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

Authors
  1. Dan Chen
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  2. Michal Fečkan
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  3. JinRong Wang
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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), the Slovak Research and Development Agency under the Contract No. APVV-18-0308, and the Slovak Grant Agency VEGA Nos. 1/0358/20 and 2/0127/20.

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Chen, D., Fečkan, M. & Wang, J. On the Stability of Linear Quaternion-Valued Differential Equations. Qual. Theory Dyn. Syst. 21, 9 (2022). https://doi.org/10.1007/s12346-021-00540-3

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