An algorithm for solving linear nonhomogeneous quaternion-valued differential equations and some open problems

Yonghui Xia; Hai Huang; Kit Ian Kou

doi:10.3934/dcdss.2021162

Article Contents

2022, Volume 15, Issue 7: 1685-1697. Doi: 10.3934/dcdss.2021162

This issue Previous Article A novel bond stress-slip model for 3-D printed concretes Next Article

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
^*Corresponding author: Yonghui Xia

Received: August 1, 2021

Revised: October 1, 2021

Early access: December 18, 2021

Published online: July 1, 2022

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Abstract

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.

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Mathematics Subject Classification: 34K23, 34D30, 37C60, 37C55, 39A12.

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