Quaternion Fractional Fourier-Laplace Transform and its Convolution Structure

Abstract

In this paper, we introduce the two-sided Quaternion Fractional Fourier--Laplace Transform (QFrFLT), an extension of the classical Fractional Fourier--Laplace Transform into the quaternion framework. We rigorously define the QFrFLT and establish its reversibility property, as well as develop an associated convolution structure along with a convolution theorem. These results not only advance the theoretical foundation of hypercomplex transforms but also demonstrate the potential of the QFrFLT for applications in multidimensional signal analysis, image processing.