Mild and classical solutions to fractional Cauchy problem on time scales.

In this manuscript, aims to examine the uniqueness and existence of impulsive non-local conditions, as well as classical and mild solutions to the fractional Cauchy problem in time scales. The main results are derived by the Gronwall inequality and the Banach fixed point theorem in time scales. Eventually, we offered an example to demonstrate the suitability of the conclusions on the fractional Cauchy issue on a time scale.

Impulsive fractional order integrodifferential equation via fractional operators.

In this paper, we establish the existence and uniqueness of the solution to fractional equations abstract integrodifferential equation with impulsive as [Formula: see text] where [Formula: see text] and we used the fixed point theorems due to Banach space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. Finally, in support, an example is presented to validate the obtained results.

A Blind Watermarking Model of the 3D Object and the Polygonal Mesh Objects for Securing Copyright.

In this paper, we propose a novel model for 3D object watermarking. The proposed method is based on the properties of the discrete cosine transform (DCT) of the 3D object vertices to embed a secret grayscale image three times. The watermarking process takes place by using the vertices coefficients and the encrypted image pixels.

Rapid and Blind Watermarking Approach of the 3D Objects Using QR Code Images for Securing Copyright.

Watermarking techniques in a wide range of digital media was utilized as a host cover to hide or embed a piece of information message in such a way that it is invisible to a human observer. This study aims to develop an enhanced rapid and blind method for producing a watermarked 3D object using QR code images with high imperceptibility and transparency. The proposed method is based on the spatial domain, and it starts with converting the 3D object triangles from the three-dimensional Cartesian coordinate system to the two-dimensional coordinates domain using the corresponding transformation matrix.