Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales

Wang, Chao; Li, Zhien; Agarwal, Ravi P.

doi:10.2478/auom-2021-0021

Abstract

In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time. Quaternion matrix combined-exponential function is introduced and some basic properties are obtained. Based on this, the fundamental solution matrix and corresponding Cauchy matrix for a class of quaternion matrix dynamic equation with combined derivatives and bi-directional impulses are derived.

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Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales

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