In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through the deviations of the transformed random process to find an efficient estimate of Hurst exponent using eigenvalue regression of the covariance matrix. The results of simulations experiments shown that the performance of the proposed estimator was efficient in bias but the variance get increase as signal change from short to long memory the MASE increase relatively. The estimation process was made by calculating the eigenvalues for the variance-covariance matrix of Meyer’s continuous wavelet details coefficients.

In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

 In this paper, we propose a method using continuous wavelets to study the multivariate fractional Brownian motion through the deviations of the transformed random process to find an efficient estimate of Hurst exponent using eigenvalue regression of the covariance matrix. The results of simulations experiments shown that the performance of the proposed estimator was efficient in bias but the variance get increase as signal change from short to long memory the MASE increase relatively. The estimation process was made by calculating the eigenvalues for the variance-covariance matrix of Meyer’s continuous wavelet details coefficients.

In our world, technological development has become inherent in all walks of life and is characterized by its speed in performance and uses. This development required the emergence of new technologies that represent a future revolution for a fourth industrial revolution in various fields, which contributed to finding many alternatives and innovative technical solutions that shortened time and space in terms of making Machines are smarter, more accurate, and faster in accomplishing the tasks intended for them, and we find the emergence of what is called artificial intelligence (artificial intelligence), which is the technology of the future, which is one of the most important outputs of the fourth industrial revolution, and artificial inte

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

 The aim of this paper, is to discuss several high performance training algorithms fall into two main categories. The first category uses heuristic techniques, which were developed from an analysis of the performance of the standard gradient descent algorithm. The second category of fast algorithms uses standard numerical optimization techniques such as: quasi-Newton . Other aim is to solve the drawbacks related with these training algorithms and propose an efficient training algorithm for FFNN

This study aims to reveal the role of one of the artificial intelligence (AI) techniques, “ChatGPT,” in improving the educational process by following it as a teaching method for the subject of automatic analysis for students of the Chemistry Department and the subject of computer security for students of the Computer Science Department, from the fourth stage at the College of Education for Pure Science (Ibn Al-Haitham), and its impact on their computational thinking to have a good educational environment. The experimental approach was used, and the research samples were chosen intentionally by the research community. Research tools were prepared, which included a scale for CT that included 12 items and the achievement test in b

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1^st and 2^nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.

Melanoma, a highly malignant form of skin cancer, affects individuals of all genders and is associated with high mortality rates, especially in advanced stages. The use of tele-dermatology has emerged as a proficient diagnostic approach for skin lesions and is particularly beneficial in rural areas with limited access to dermatologists. However, accurately, and efficiently segmenting melanoma remains a challenging task due to the significant diversity observed in the morphology, pigmentation, and dimensions of cutaneous nevi. To address this challenge, we propose a novel approach called DenseUNet-169 with a dilated convolution encoder-decoder for automatic segmentation of RGB dermascopic images. By incorporating dilated convolution,