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.

The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil

Infertility is one of the types of diseases that occur in the reproductive system. Obesity is a state that can be occurred due to excessive fats, the progression in obesity stage results in a change in adipose tissue and the development of chronic inflammation, endocrine glands disorders and women’s reproductive system, and also increase the infection with covid-19. The study aimed to investigate the effect of the obesity, lipid-profile, and IL-6 on hormones-dysregulation in infertile-women with COVID-19 complications. The current study included 70 samples: 50 infertility-women-with-covid-19-infected, 20 healthy-women/control, the ages of both patients and healthy subjects were selected within the range 18-34 years. Levels of FBS, LH,

A cumulative review with a systematic approach aimed to provide a comparison of studies’ investigating the possible impact of the active form of vitamin D3, calcitriol (CTL), on the tooth movement caused by orthodontic forces (OTM) by evaluating the quality of evidence, based on collating current data from animal model studies, in vivo cell culture studies, and human clinical trials. Methods: A strict systematic review protocol was applied following the application of the International Prospective Register of Systematic Reviews (PROSPERO). A structured search strategy, including main keywords, was defined during detailed search with the application of electronic database systems: Medline/Pubmed, EMBASE, Scopus, Web of Science, and

         The studying trying to determine the role of  Strategic Intelligence on the Process of Green Manufacturing  of  Sample of Mineral water factories at Dahuk city.  The study submit a theoretical frame of Strategic Intelligence and Green Manufacturing, a supposed sample, had been set to reverye   the nature of the relations and effect in the study  Varity, the study  depend on group of the main and branch concurring with the relations and effect between the Strategic Intelligence and Green Manufacturing to answer the following questions about research to problems:

 What are the relationships and effects between stra

At the beginning of 1935 theMinistry of (Yasin AL-Hashimi) was formed which was the result of the (Sulayikh)Conference .The new ministys policy was towards the authority of the one party and the exclusivity of power.The policy of (Yasin AL-Hashemi)has faced severe campaigns from the AL-Ekhaa and AL-Ahaly newspapers.The new ministry like its predecessor ministries . When it faces criticism from opposition newspapers .its shutting down newspapers and not accepting requests for them. Some opposition newspapers named Yassin AL-Hashemi (the dictator).Iraqi opposition newspapers have been neglected and deprived of press freedom although they were the main factor in educating the community and representing the public opinion of people . Lt appe