One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations

Abstract

This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation theorems are quite different from the corresponding properties of the classical Laplace transform. Other properties like linearity, shifting, scaling and derivative are also studied in detail. Finally, the utility of the quaternion Laplace transform for solving quaternion-valued differential equations is presented.

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