The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

Background: One of the drawbacks of vital teeth bleaching is color stability. The aim of the present study was to evaluate the effects of tea and tomato sauce on the color stability of bleached enamel in association with the application of MI Paste Plus (CPP-ACPF). Materials and Methods: Sixty enamel samples were bleached with 10% carbamide peroxide for two weeks then divided into three groups (A, B and C) of 20 samples each. After bleaching, the samples of each group were subdivided into two subgroups (n=10). While subgroups A1, B1 and C1 were kept in distilled water, A2, B2, and C2 were treated with MI Paste Plus. Then, the samples were immersed in different solutions as follow: A1 and A2 in distilled water (control); B1 and B2 in black

What is important about this study is whether there is a relationship between the ability to balance and beating overwhelming for the Iraqi national team volleyball? The study aims to identify the percentage of the equilibrium contribution and its variables with the accuracy of the skill of beating the high spike Diagonal center (4) in the players. In the national volleyball team season (2016-2017), the researchers used the descriptive approach in the style of associative relationships to suit the problem of research. The research community included all the players specialized in the high beating of the Iraqi national team applicants in the ball The researchers concluded that the equilibrium variables contributed accurately and quickly to t

The rapid developmemt of information technology and its use in all fields has a bositive influence on all fields , and financial markets have a share of this development through the use of an electronic trading system to settle transactions and enhance transparency and disclosure in all activities of these markets and stimulate their performance .

It is worth nothing that these revolutions remove the necessity for nonstop connection with persons through the internet or phone networks , novel knowledge decreases the charges of structure original transaction system and reducing the fences of new participants entry .

The development in transportations expertise allows for quicker or

The study was conducted to assess the attitude and awareness of a sample of people regarding the indiscriminate slaughter and its effects on health and the environment compared with slaughtering  in a slaughterhouse. The sample consisted of 120 persons from six equal professional groups contacted with the butchery labour (livestock keeper, truck driver, butcher, veterinarian, shopkeeper and consumer). The age ranged 22-76 years old, mean 52±10  years, lived ≥ 5 years in the Baghdad city. The results showed that there is a preference for slaughtering inside the slaughterhouse due to the presence of veterinary examination, slaughtering and preparing meat in a healthy, easy-to-clean places, unlike the indiscriminate sla

Many countries are very important in their interest not only in diversifying foreign reserves, but in determining and planning their volume in accordance with the goals set, namely facing potential external shocks, as the research aims to determine the extent of the strength of foreign reserves in the possession of the Central Bank in relation to every influential variable in the Iraqi economy. , in order to determine the minimum level of reserves that requires reconsideration of the exchange rate, as the research adopted the inductive analytical method in analyzing real (Quantitative data) for the research variables in the years of study, as the research adopted a set of analytical indicators approved by the International Moneta

The research aimed to determine the role of the agricultural extension in educating farmers about the legislation on the protection of the rural environment from pollution with chemical pesticides working in the Department of Agricultural Extension and Training and the Department of Agricultural Extension in the directorates of agriculture of Najaf and Qadisiyah, and to determine the role of the agricultural extension in the axis of farmers' use of the correct methods to protect the rural environment from pollution with chemical pesticides and the axis of the reasons that lead farmers to pollute the rural environment with chemical pesticides, and to achieve the objectives of this research prepared A questionnaire in the light of rev