It is well known that the Fourier transform is a special case of the linear canonical transform. Therefore, most properties of the linear canonical transform are extensions of the corresponding properties of the Fourier transform. Due to its usefulness and applications in many fields of applied mathematics, optics, and digital information processing, various kinds of transformations have been developed using the linear canonical transform.

Recently, the quaternion linear canonical transform has been introduced, including its fundamental properties such as convolution, correlation, and uncertainty principles. Several researchers also have proposed the quaternionic windowed linear canonical transform, which is an extension of the windowed Fourier transform using quaternionic linear canonical transform. Some essential properties of the new transform, such as shifting, modulation, and inequalities were obtained. Other properties and applications are still being investigated and further developed.

The purpose of this Special Issue is to publish developments in current theories and applications of linear canonical transforms, Stockwell, fractional Fourier, and wavelet transforms, and fractional integral operators. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Stockwell, Fourier, and wavelet transforms in the linear canonical transform and fractional Fourier transform domains
• Development of Wigner –Ville distribution associated with the linear canonical transform and applications
• Windowed Fourier transforms associated with linear canonical transforms and applications
• Development of the quaternion Fourier transform and applications
• Quaternion windowed Fourier transform and applications
• Uncertainty principles for the quaternion linear canonical transform
• Convolution and correlation theorems of the quaternion linear canonical transform
• Clifford linear canonical transforms and Clifford fractional Fourier transforms
• Stockwell transforms in Clifford algebra
• Development of fractional integral operators