Quaternion-Valued Linear Impulsive Differential Equations

• Suo, Leping ^[1] ; Fečkan, Michal ^[2] ; Wang, JinRong ^[3]
  1. [1] Guizhou University

     Guizhou University

     China

     
  2. [2] Comenius University

     Comenius University

     Eslovaquia

     
  3. [3] Guizhou University & Qufu Normal University

  Mostrar afiliaciones +
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 2, 2021
• Idioma: inglés
• DOI: 10.1007/s12346-021-00467-9
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we transfer the approach of finding the explicit solutions to linear impulsive differential equations (LIDEs) to quaternion-valued case. We develop the similar idea to find the solutions to LIDEs and give the details to derive the representations of the solutions to quaternion-valued LIDEs in the sense of complex numbers and quaternion. In addition, we present that two formulas are equivalent to each other. Finally, some examples are given to illustrate the theory approach.

• Referencias bibliográficas
  • Xia, Y.H., Huang, H., Kou, K.I.: An algorithm for solving linear nonhomogeneous quaternion-valued differential equations (2016). arXiv:1602.08713v2
  • Zhu, J.W., Sun, J.T.: Existence and uniqueness results for quaternion-valued nonlinear impulsive differential systems. J. Syst. Sci. Complex....
  • Cheng, D., Kou, K.I., Xia, Y.H.: Floquet theory for quaternion-valued differential equations. Qual. Theory Dyn. Syst. 19, 1–23 (2020)
  • Cai, Z.F., Kou, K.I.: Laplace transform: a new approach in solving linear quaternion differential equations. Math. Methods Appl. Sci. 41,...
  • Kou, K.I., Liu, W.K., Xia, Y.H.: Linear quaternion differential equations: basic theory and fundamental results (II) (2016). arXiv:1602.01660v3
  • Kou, K.I., Xia, Y.H.: Linear quaternion differential equations: basic theory and fundamental results. Stud. Appl. Math. 141, 3–45 (2018)
  • Kou, K.I., Liu, W.K., Xia, Y.H.: Solve the linear quaternion-valued differential equations having multiple eigenvalues. J. Math. Phys. 60,...
  • Cai, Z.F., Kou, K.I.: Solving quaternion ordinary differential equations with two-sided coefficients. Qual. Theory Dyn. Syst. 17, 441–462...
  • Zhang, F., Wei, Y.: Jordan canonical form of a partioned complex matrix and is application to real quatenion matrices. Commun. Algebra 29,...