# American Institute of Mathematical Sciences

doi: 10.3934/dcdss.2021162
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## An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems

 1 College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China 2 School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China 3 Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau 999078, China

*Corresponding author: Yonghui Xia

Received  August 2021 Revised  October 2021 Early access December 2021

Quaternion-valued differential equations (QDEs) is a new kind of differential equations. In this paper, an algorithm was presented for solving linear nonhomogeneous quaternionic-valued differential equations. The variation of constants formula was established for the nonhomogeneous quaternionic-valued differential equations. Moreover, several examples showed the feasibility of our algorithm. Finally, some open problems end this paper.

Citation: Yonghui Xia, Hai Huang, Kit Ian Kou. An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2021162
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