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.

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In this search, we examined the factorial experiments and the study of the significance of the main effects, the interaction of the factors and their simple effects by the F test (ANOVA) for analyze the data of the factorial experience. It is also known that the analysis of variance requires several assumptions to achieve them, Therefore, in case of violation of one of these conditions we conduct a transform to the data in order to match or achieve the conditions of analysis of variance, but it was noted that these transfers do not produce accurate results, so we resort to tests or non-parametric methods that work as a solution or alternative to the parametric tests , these method

Sustainable crop production in a coarse soil texture is challenging due to high water permeability and low soil water holding capacity. In this paper, subsurface water retention technology (SWRT) through impermeable polyethylene membranes was placed at depth 35 cm below ground surface and within the root zone to evaluate and compare the impact of these membranes and control treatment (without using the membranes) on yield and water use efficiency of eggplant inside the greenhouse. The study was conducted in Al-Fahamah Township, Baghdad, Iraq during spring growing season 2017. Results demonstrated the yield and water use efficiencies were 3.483 kg/m² and 5.653 kg/m³, respectively for SWRT treatment p

Background: obesity is a major global health problem with more than 200 million obese men and almost 300 million obese women. Melatonin is a well-known molecule for its involvement in circadian rhythm regulation and has multiple pathological actions including control of appetite, sleep wake cycle and metabolic syndrome.

Aim: to estimate the effect of melatonin supplements on obese patients on a calorie restricted diet in comparison to patients on lifestyle measures only in the form of weight loss, waist circumference and sleep quality.

Subjects and Method: one hundred patients with body mass index > 24 were collected, fifty patients were starte

Background: The purpose of this study was to compare regional bond strength at middle and cervical thirds of the root canal among glass fiber-reinforced composite (FRC) endodontic posts cemented with different cements, using the push-out test to compare the performance (retention) of two types of luting cements; polycarboxylate cement and Zinc phosphate cement used to cement translucent fiber post and to compare the result of the push-out test at different storage times;1 week ,1month and 2 months. Materials and methods: Ninety caries-free, recently extracted single-rooted human teeth with straight root canals was used in this study, The root canals were endodontically instrumented at a working length of 0.5 mm from the apex by m

Rotaviruses, a major cause of gastroenteritis in children worldwide accounts for around half a million deaths annually. Vaccine against the virus has been recommended by the WHO to be involved in the national immunization program.To evaluate the genetic characterization of rotavirus among children with acute gastroenteritis in Babylon province is warranted. Children complained of diarrhea with rotavirus infection detected in their stool were involved in the study. The age range was 10 months to 60 months and with retrogradechecking of rotavirus vaccine history. Rotavirus genotypes were detected by reverse transcription-polymerase chain reaction (RT-PCR).A total number of 40 children with rotavirus gastroenteritis were used to examine the