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Hyers-Ulam Stability of Linear Quaternion-Valued Differential Equations with Constant Coefficients via Fourier Transform

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Abstract

In this paper, we develop the Fourier transform approach to study the Hyers-Ulam stability of linear quaternion-valued differential equation with real coefficients and linear quaternion-valued even order differential equation with quaternion coefficients. It shows that Fourier transform is valid to find the approximate solutions for quaternion-valued differential equations by considering their corresponding complex representation of quaternion-valued problems. Finally, two examples are given to illustrate the theoretically 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

    Jiaojiao Lv & JinRong Wang

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

    Kit Ian Kou

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  1. Jiaojiao Lv
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  2. Kit Ian Kou
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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), 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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Lv, J., Kou, K.I. & Wang, J. Hyers-Ulam Stability of Linear Quaternion-Valued Differential Equations with Constant Coefficients via Fourier Transform. Qual. Theory Dyn. Syst. 21, 116 (2022). https://doi.org/10.1007/s12346-022-00649-z

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  • DOI: https://doi.org/10.1007/s12346-022-00649-z

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