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Representation of Solutions to Linear Quaternion Differential Equations With Delay

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Abstract

In this paper, linear quaternion differential equations (LQDEs) with delay attracts our attention. In the light of delayed quaternion matrix exponential and the method of variation of constants, we derive the solutions of homogeneous and nonhomogeneous LQDEs with delay under the assumption of permutation matrices. Further, we investigate the solutions of homogeneous and nonhomogeneous LQDEs with delay without the requirement of permutation matrices. Finally, examples illustrate the validity of the results.

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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, Guizhou, 550025, China

    Teng Fu & JinRong Wang

  2. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, China

    Kit Ian Kou

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  1. Teng Fu
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  2. Kit Ian Kou
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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), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), Major Project of Guizhou Postgraduate Education and Teaching Reform (YJSJGKT[2021]041), Science and Technology Development Fund, Macao S.A.R (FDCT/0036/2021/AGJ) and Science and Technology Planning Project of Guangzhou City, China [Grant No. 201907010043]

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Fu, T., Kou, K.I. & Wang, J. Representation of Solutions to Linear Quaternion Differential Equations With Delay. Qual. Theory Dyn. Syst. 21, 118 (2022). https://doi.org/10.1007/s12346-022-00648-0

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