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.

Social risks posed a great challenge to the development path in Iraq, which resulted in widening the development gaps, whether these gaps were between rural and embargoed areas, or between Iraqi governorates, and the gender gap. Besides, the nature of the reciprocal relationship between the social risks and the development process requires the adoption of development trends that are sensitive to the risks that take upon themselves the prompt and correct response to these risks, away from randomness and confusion that Iraq suffered from for decades. However, currently, the situation has differed a great deal. This is because the size and types of such gaps have widened and become more complicated than before; a matter which has led to hav

This research is a new reading of some of the words in the Holy Quran, which is very old. It is a human reading in which religions are intertwined by recognizing the relationship between man and his fellow man in the unity of existence and the unity of the source of religions and the unity of language. The importance of this research in comparing some of the Arabic words has been contained among books believed by followers that it is from the one God Sunday.

When words are spoken in one way in the form of one creature, from the beginning of creation to the present day, this indicates the single origin of the languages..

The research tools were books of heavenly religions, the Quran, dictionaries and interpretations.

A novel technique Sumudu transform Adomian decomposition method (STADM), is employed to handle some kinds of nonlinear time-fractional equations. We demonstrate that this method finds the solution without discretization or restrictive assumptions. This method is efficient, simple to implement, and produces good results. The fractional derivative is described in the Caputo sense. The solutions are obtained using STADM, and the results show that the suggested technique is valid and applicable and provides a more refined convergent series solution. The MATLAB software carried out all the computations and graphics. Moreover, a graphical representation was made for the solution of some examples. For integer and fractional order problems, solutio

The American playwright Stephen Karam explores the human psyche and relationships in The Humans (2016) by employing the spatial operations of the props on the stage. The play presents the gathering of the Blake family in their daughter and her boyfriend's new apartment on a Thanksgiving dinner. The article examines how the description of the details of the place reflects the characters' fear, pain, trauma, relationships and secrets. It aims to show how the characters' psychologies are depicted through the physical setting of the dark apartment and its menacing atmosphere. The study follows the theory of place in approaching the text. It tries to analyze the relationship between the place and the characters and how it develops a type

Atmospheric transmission is disturbed by scintillation, where scintillation caused more beam divergence. In this work target image spot radius was calculated in presence of atmospheric scintillation. The calculation depend on few relevant equation based on atmospheric parameter (for Middle East), tracking range, expansion ratio of applied beam expander's, receiving unit lens F-number, and the laser wavelength besides photodetector parameter. At maximum target range Rmax =20 km, target image radius is at its maximum Rs=0.4 mm. As the range decreases spot radius decreases too, until the range reaches limit (4 km) at which target image spot radius at its minimum value (0.22 mm). Then as the range decreases, spot radius increases due to geom

This study examines experimentally the performance of a horizontal triple concentric tube heat exchanger TCTHE made of copper metal using water as cooling fluid and oil-40 as hot fluid. Hot fluid enters the inner annular tube of the TCTHE in a direction at a temperature of 50, 60 and 70 ^oC and a flow rate of 20 l/hr. On the other hand, the cooling fluid enters the inner tube and the outer annular tube in the reverse direction (counter current flow) at a temperature of 25 ^oC and flow rates of 10, 15, 20, 25, 30 and 35 l/hr. The TCTHE is composed of three copper tubes with outer diameters of 34.925 mm, 22.25 mm, and 9.525 mm, and thicknesses of 1.27 mm, 1.143 mm, and 0.762 mm, respectively. TCTHE tube's length was 670