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.

الخلاصة

تشير نظريات علم اجتماع المعرفة الى ان ظهور مفهوم معين او سقوطه لايتم بمحض الصدفة، بل نتيجة تفاعل مجموعة من العوامل الثقافية والسياسية وحتى الاقتصادية ومن هنا فأن ظهور مفهوم الاثنية كان محصلة عوامل كثيرة خصوصاً بعد ان اصبح موضوع الاثنية في العقود الاخيرة من القرن الماضي وبداية القرن الواحد والعشرين محور نقاش رئيس في ميدان البحث الاجتماعي والسياسي، ليس في

In this paper, the using of Non-Homogenous Poisson Processes, with one of the scientific and practical means in the Operations Research had been carried out, which is the Queuing Theory, as those operations are affected by time in their conduct by one function which has a cyclic behavior, called the (Sinusoidal Function). (M_t / M / S) The model was chosen, and it is Single Queue Length with multiple service Channels, and using the estimating scales (QL_s, HOL, HOL_r) was carried out in considering the delay occurring to the customer before his entrance to the service, with the comparison of the best of them in the cases of the overload.

Through the experiments

The study aims to identify the impact of electronic games on increasing the dropout rate among students in the basic stage in Jordan from their teachers’ point of view. The study adopted a descriptive survey method. Its community consisted of all fe(male) teachers of the basic stage in public and private schools, (First Amman, Irbid, and special education in Zarqa and Amman). The electronic questionnaire was used as a tool for the study. The results have shown that the effect of electronic games on increasing the dropout rate among students in the basic stage in Jordan was high. Besides, there are statistically significant differences due to the gender variable for males. There are statistically significant differences due to the varia

The Study addressed the effectiveness of dialogic communication in online public relations with an audience of higher education institutions in the United Arab Emirates. The study aimed to know about the interest extent of higher education institutions through their websites with the elements of dialogic communication in online public relations to communicate with their audience. The researcher used survey methodology and content Analysis tool as an essential tool for collecting information. Some of the important results of the study are: The websites of higher education institutions in terms of indicators of ease of use; the main links on the websites are clearly available on the opening page, there is a map on the websites, reduce depe

   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.  

The present theoretical study analyzes the legacy of the Chicago School of Urban Sociology and evaluates it in the light of the growth and development of Chicago City and the establishment of sociology in it. Sociology has become an academic discipline recognized in the United States of America in the late nineteenth century, particularly, after the establishment of the first department of sociology in the University of Chicago in 1892. That was during the period of the rapid industrialization and sustainable growth of the Chicago City. The Chicago School relied on Chicago City in particular, as one of the American cities that grew and expanded rapidly in the first two decades of the twentieth century. At the end of the nineteenth centur

Several stress-strain models were used to predict the strengths of steel fiber reinforced concrete, which are distinctive of the material. However, insufficient research has been done on the influence of hybrid fiber combinations (comprising two or more distinct fibers) on the characteristics of concrete. For this reason, the researchers conducted an experimental program to determine the stress-strain relationship of 30 concrete samples reinforced with two distinct fibers (a hybrid of polyvinyl alcohol and steel fibers), with compressive strengths ranging from 40 to 120 MPa. A total of 80% of the experimental results were used to develop a new empirical stress-strain model, which was accomplished through the application of the parti

        The research aimed to compare the performance of the commercial and the  Islamic banks listed in the Palestinian's Stock Exchange .To achieve the objectives of the study we selected all  the commercial and the Islamic banks listed in the Palestinian Stock Exchange  to obtain the necessary data for the analysis process during the period of (2009-2013) .the comparison based on the performance indicators ( liquidity rate, profitability rate ,the activity rate and the market rate).

        a statistical method was used to analyze the date to find the performance differences between the commercial banks,

Polycystic ovary syndrome (PCOS) is the main cause of female infertility. The role of insulin resistance in the development of polycystic ovary is actively discussed here. The study included patients with PCOS without insulin resistance (n = 48) and with insulin resistance (n = 39). The comparison groups were patients with no history of PCOS: a control group without insulin resistance (n = 46) and a group of patients with insulin resistance (n = 45). The following parameters were determined in patients: FSH, LH, TSH, T3_f, T4_f, PRL, E2, 17-OHd, Pr, AMH, Test total, Test_f, DHEAS, DHEAS_s, SHBG, ACTH, cortisol, IRI, IGF-1, C-peptide, and glucose level. The HOMA-IR index and the LH / FSH ratio and t