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.

In this study, a mathematical model is presented to study the chemisorption of two interacting atoms on solid surface in the presence of laser field. Our mathematical model is based on the occupation numbers formula that depends on the laser field which we derived according to Anderson model for single atom adsorbed on solid surface. Occupation numbers formula and chemisorption energy formula are derived for two interacting atoms (as a diatomic molecule) as they approach to the surface taking into account the correlation effects on each atom and between atoms. This model is characterized by obvious dependence of all relations on the system variables and the laser field characteristics which gives precise description for the molecule –

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The issue of the protection of the environment is a shared responsibility between several destinations and sectors, and constitutes a main subject in which they can achieve sustainable development. In the sectors of government programs can be set up towards the establishment of the government sector to the green environment, so to be the implementati

In this paper, an eco-epidemiological prey-predator system when the predator is subjected to the weak Allee effect, and harvesting was proposed and studied. The set of ordinary differential equations that simulate the system’s dynamic is constructed. The impact of fear and Allee’s effect on the system's dynamic behavior is one of our main objectives. The properties of the solution of the system were studied. All possible equilibrium points were determined, and their local, as well as global stabilities, were investigated. The possibility of the occurrence of local bifurcation was studied. Numerical simulation was used to further evaluate the global dynamics and understood the effects of varying parameters on the asymptotic behavior of t

Abstract:

    Under the state scenario, fiscal policy will not be able to use the oil surpluses optimally and economically and society, as long as these surpluses are not directed by public expenditure towards new productive investments and by following the path of fiscal policy after one year 2003 and until 2013 we note that it is based on the method of spending (excessive) consumption, and did not take any action towards the budget deficit planned at the beginning of the fiscal year, and the actual surplus at the end of the fiscal year, which represents the highest expenditure in the budget, Salaries and wages of workers in various government agencies with the expansion of spending on the security side.&n

   Increasingly, public organizations in the federal state are required to work together, as well as to work with others to achieve their objectives. In Iraq there are two levels of organizations, including federal and local, and these organizations have been forced to work for many years in an environment in which the responsibility for service delivery is shared between policy makers and service providers, and between local governments and the federal government. It is sometimes difficult to manage the relationship between these organizations (federal and local) and do not always provide the best possible outcome of this relationship. This paper reviews how to manage the relationship between local administrations and

The interaction of charged particles with the chemical elements involved in the synthesis of human tissues is one of the modern techniques in radiation therapy. One of these charged particles are alpha particles, where recent studies have confirmed their ability to generate radiation in a highly toxic localized manner because of its high ionization and short its range. In this work, We focused our study on the interaction of alpha particles with liquid water; since the water represents over 80% of the most-soft tissues, as well as, hydrogen, oxygen, and nitrogen ,because they are key chemical elements involved in the synthesis of most human tissues. The mass stopping powers of alpha particle with HଶO , COଶ, Oଶ, Hଶ and Nଶhave

Represent a topic occupational safety and health management is one of the priorities of the loading organization in the business environment ,and one of the requirement for the success and its impact on the productivity of workers and their performance in an appropriate working environment .The international responses to the problems that accompany the technological and industrial development of the business environment are the issuance of ISO 45001:2018 aimed at providing an appropriate framework for controlling risks , reducing injuries and work accidents and improving work performance ,after realizing the environmental relationship between safe and sound work with competition .The search’s issue is represented with the exist