There exists a fractional Fourier-transform relation between the amplitude distributions of light on two spherical surfaces of given radii and separation. The propagation of light can be viewed as a process of continual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through fractional transforms of increasing order. This result allows us to pose the f...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

We describe the implementation of a watermark embedding technique for images using the discrete fractional Fourier transform. The idea is that a 2D discrete fractional Fourier transform of the image is computed. In this transform domain, a normal distributed random sequence with certain characteristics is used to modify the transform coefficients in the middle range of magnitude. Then the inver...

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRS...

Abstract: In this paper, we study the approximation of analytical solution for Fractional Reaction Diffusion model which describes the evaluation of bacterium Bacillus, which grows on the surface of thin agar plates, by using homotopy analysis transform method. The fractional derivatives are described by caputo sense. A comparative study between the homotopy analysis transform method and the cl...

A new image encryption scheme based on logistic map and discrete fractional angular transform has been proposed. In the proposed scheme, the original image is encrypted with the random sequence generated by the logistic map, and the encrypted image is subsequently processed by the discrete fractional angular transform, which produces the ciphertext after double encryptions. The parameters of th...

Based on an all-optical system, a display of a fractional Fourier transform with many fractional orders is proposed. Because digital image-processing terminology is used, this display is known as the Radon-Wigner transform. It enables new aspects for signal analysis that are related to time- and spatial-frequency analyses. The given approach for producing this display starts with a one-dimensio...

The proposed research paper shall analyze a method of image change detection based upon the Fractional Fourier transform (FrFT), which can provide results with good precision and better recall values obtained by optimizing its fractional order 'a'. The method is analyzed because, with extra degree of freedom provided by the Discrete Fractional Fourier Transform (DFrFT), we can get mor...

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by...