Solving quaternionic differential equations with the renewal mathematical methods

The recent results on quaternionic differential operators which can be applied to quantum mechanics, in particular tunneling effects and robotic dynamics interested in the study of resolution methods for quaternionic differential equations. In this paper, by using the real matrix representation of quaternionic operators, we propose the reduction of order for quaternionic homogeneous differential equations and extend to the noncommutative case the method of variation of parameters. Also, we show that the modified complex Wronskian admits a noncommutative extension for quaternionic functions of a quaternionic variable. Specially, we present quaternionic second order differential equations and obtain the result that linear dependence and independence of solutions of homogeneous linear differential equations.
This work is supported by the Dongguk University Research Fund and the National Research Foundation of Korea (NRF) (2017R1C1B5073944).