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.

Abstract 

     This research aims to analyze the reality of the production process in an assembly line Cars (RUNNA) in the public company for the automotive industry / Alexandria through the use of some Lean production tools, and data were collected through permanence in the company to identify the problems of the line in order to find appropriate to adopt some Lean production tools solutions, and results showed the presence of Lead time in some stations, which is reflected on the customer's waiting time to get the car, as well as some of the problems existing in the car produced such as high temperature of the car, as the company does not take into account customer preferences,

Material Requirements Planning System (MRP) is considered as one of the planning and controlling of production and inventory systems which is used to prepare plan of the final production requirements and its parts of subcomponents raw materials and the time at which it was needed for the purpose of preparing orders of production and purchase.

The problem of the present work is represented in the general company of electrical industrialization adoption of traditional methods and personal experience of the process of the products and\or purchase quantity and inventory quantities and limiting the required time for acquiring the required quantities of the materials and parts used in the finish product of the

This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),

The banking sector is currently facing great challenges resulting from intense competition in the financial environment, and this is what makes the supreme audit bodies and the Central Bank audit as the highest supervisory authority on banks in order to achieve profit and not be exposed to loss, and this requires identifying the banking strengths and risks that constitute points Weakness that affects the future performance and the life of the bank, which requires special supervisory care, and from this point of view, the research aims to use the CAMELS model as a control tool in banks, through the use of its six indicators: capital adequacy, asset quality, management quality, profits, liquidity And sensitivity to market risks, th