Fractional Integral Transforms: Theory and Applications

Dear Colleagues,

Integral transforms have played a vital role in mathematics and physics for more than two centuries. Two of the oldest and most widely used transforms are the Laplace and Fourier transforms, which have numerous applications in physics and engineering. In the last forty years or so, the notion of fractional integral transforms has emerged on the scene as an extension of the classical transforms with potential for many more applications.

One of the earliest fractional integral transforms is the fractional Fourier transform (FrFT), which is a generalization of the Fourier transform. Because the FrFT has proven to be a very useful mathematical tool in phase-space representation, signal and image processing, and optics, other generalizations of classical transforms were introduced, such as fractional Hankel and Radon transforms, fractional continuous wavelet transforms, as well as the linear canonical and the special affine Fourier transforms, all of which have proven to have real-world applications.

Many properties of these fractional transforms have been studied, such as their inversion formulas, convolution structures, associated sampling theorems, and their properties as operators acting on functions spaces. The extension of some of these properties to higher dimensions is somewhat challenging, but considerable progress has been achieved.

The aim of this Special Issue is to compile frontier work on the theory and applications of fractional integral transforms. Theoretical work may include but not be limited to analytic properties, multidimensional extensions, function spaces, sampling theorems, and operator theory. Research and review articles on applications of fractional integral transforms in various fields, in particular in optics, signal, and image processing, is welcome.

Prof. Dr. Ahmed I. Zayed
Guest Editor

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• Fractional integral transforms
• Fractional Fourier transform
• Linear canonical transform
• Special affine Fourier transform
• Shift-invariant spaces
• Sampling theorems