# One-dimensional quaternion Laplace transform: Properties and its application to quaternion-valued differential equations
> Bau M.A.

URL kanonis: https://discover.unhas.ac.id/publications/one-dimensional-quaternion-laplace-transform-properties-and-its-application-to-q
Jurnal / Konferensi: Partial Differential Equations in Applied Mathematics
Tahun terbit: 2023
DOI: https://doi.org/10.1016/j.padiff.2023.100547
Kuartil SJR: Q2
Citations: 6

## Authors
- Bau M.A.

## 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.

## Keywords
- Quaternion
- Laplace transform
- Mathematics
- Laplace transform applied to differential equations
- Two-sided Laplace transform
- Convolution (computer science)
- Convolution theorem
- Mathematical analysis
- Inverse Laplace transform
- Generalization
- Applied mathematics
- Fourier transform
- Fractional Fourier transform
- Computer science
- Geometry
- Artificial intelligence
- Artificial neural network
- Fourier analysis

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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