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.

%8 2018-07 %D 2018 %I SPRINGER BASEL AG %J QUALITATIVE THEORY OF DYNAMICAL SYSTEMS %P 441-462 %V 17 %@ 1575-5460 %U http://repository.umac.mo/handle/10692/426 %W UM