Abstract
The theory of quaternion differential equations (QDEs) has recently received a lot of attention. They have numerous applications in physics and engineering problems. In the present investigation, a new approach to solve the linear QDEs is achieved. Specifically, the solutions of QDEs with two-sided coefficients are studied via the adjoint matrix technique. That is, each quaternion can be uniquely expressed as a form of linear combinations of two complex numbers. By applying the complex adjoint representation of quaternion matrix, the connection between QDEs, with unilateral or two-sided coefficients, and a system of ordinary differential equations is achieved. By a novel specific algorithm, the solutions of QDEs with two-sided coefficients are fulfilled.
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Acknowledgements
Funding was provided by Universidade de Macau (Grant No. MYRG2015-00058-FST), National Natural Science Foundation of China (Grant Nos. 11401606, 11501015). Science and Technology Development Fund (Grant Nos. FDCT/099/2012/A3, FDCT/031/2016/A1).
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Cai, Z.F., Kou, K.I. Solving Quaternion Ordinary Differential Equations with Two-Sided Coefficients. Qual. Theory Dyn. Syst. 17, 441–462 (2018). https://doi.org/10.1007/s12346-017-0246-z
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DOI: https://doi.org/10.1007/s12346-017-0246-z