Two-sided fractional quaternion Fourier transform and its application
Journal of Inequalities and Applications , Volume 2021, pp 1-15; https://doi.org/10.1186/s13660-021-02654-3
Abstract: In this paper, we introduce the two-sided fractional quaternion Fourier transform (FrQFT) and give some properties of it. The main results of this paper are divided into three parts. Firstly we give a definition of the FrQFT. Secondly based on properties of the two-sided QFT, we study the relationship between the two-sided QFT and the two-sided FrQFT, and give some differential properties of the two-sided FrQFT and the Parseval identity. Finally, we give an example to illustrate the application of the two-sided FrQFT and its inverse transform in solving partial differential equations.
Keywords: Two-sided fractional quaternion Fourier transform / Differential properties / Parseval identity / Partial differential equations
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