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 research deals with the relationship between supplier evaluation (single variable) and family brand strategy (single variable) a case study in the battery factory\Al-Waziriya, and the fact that the industrial sector represents a cornerstone for building the country’s economy of and their development. The research has been selected on this basis. The problem stems from the lack of business understanding of the real role played by the assessment of the suppliers' and its strong impact on its reputation and position in the market. The research gains its importance by moving away from traditional marketing style in terms of characteristics related to the resource itself, and the service provided by the factory to c

— To identify the effect of deep learning strategy on mathematics achievement and practical intelligence among secondary school students during the 2022/2023 academic year. In the research, the experimental research method with two groups (experimental and control) with a post-test were adopted. The research community is represented by the female students of the fifth scientific grade from the first Karkh Education Directorate. (61) female students were intentionally chosen, and they were divided into two groups: an experimental group (30) students who were taught according to the proposed strategy, and a control group (31) students who were taught according to the usual method. For the purpose of collecting data for the experimen

A new blind restoration algorithm is presented and shows high quality restoration. This
is done by enforcing Wiener filtering approach in the Fourier domains of the image and the
psf environments

The aim of this research is to apply Throughput Accounting in improving the cost leadership strategy for the woven fabric department (polyester blended - polyester 150/1) in the Waist Textile and Knitting Factory. The problem of the research is that the research sample laboratory does not apply modern cost management methods represented in Throughput Accounting, as the Iraqi economic units suffer from their inability to compete in the labor market in light of the competitive environment. The Ministry of Interior improved the cost leadership strategy for the product of blended polyester and polyester fabrics 1/150. Through the research, a set of conclusions was reached, the most important of which are:  Improving the cost lea

This paper presents a cognition path planning with control algorithm design for a nonholonomic wheeled mobile robot based on Particle Swarm Optimization (PSO) algorithm. The aim of this work is to propose the circular roadmap (CRM) method to plan and generate optimal path with free navigation as well as to propose a nonlinear MIMO-PID-MENN controller in order to track the wheeled mobile robot on the reference path. The PSO is used to find an online tune the control parameters of the proposed controller to get the best torques actions for the wheeled mobile robot. The numerical simulation results based on the Matlab package show that the proposed structure has a precise and highly accurate distance of the generated refere

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of 

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.