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 paper aims to build a model that supports organizational sustainability by analyzing the correlations and revealing the impact between the two main variables (entrepreneurial leadership) with its dimensions of proactive outlook, risk, and creativity (Van Zyl & Mathur-Helm, 2007), and (organizational sustainability) with its economic, environmental, and societal dimensions (Hansmann et al., 2012). As well as identifying the level of awareness and informing managers in the General Company for the Automotive and Equipment Industry, of the theoretical implications and performance, and its vital importance to society and the surrounding ecological environment, and drawing attention to that and improving performance, and indicatin

This study aimed at identifying how children express the emerging coronavirus in general and according to their age groups (4-13 years) by analyzing 91 of their drawings published online, using the descriptive content analytical approach. The results showed that children's artistic expression of the virus came according to the concepts and ideas they carried about the virus for the age groups of (4-7 years) and (7-9 years), while it came according to visual perception for age groups (9-11 years), and from (11-13) years. Also, most children were aware about the presence of the virus and its widespread around the world, but (99%) of them do not realize the seriousness of the virus. It was confirmed that between (25-34%) of children were su

Abstract: The increased interest in developing new photonic devices that can support high data rates, high sensitivity and fast processing capabilities for all optical communications, motivates a pre stage pulse compressor research. The pre-stage research was based on cascading single mode fiber and polarization maintaining fiber to get pulse compression with compression factor of 1.105. The demand for obtaining more précised photonic devices; this work experimentally studied the behavior of Polarization maintaining fiber PMF that is sandwiched between two cascaded singe mode fiber SMF and fiber Bragg gratings FBG. Therefore; the introduced interferometer performed hybrid interference of both Mach-Zehnder

Abstract: In the present work, the heat transfer of Nano Aluminum Oxide -NAO- has been studied practically to define the appropriate insulation conditions.  This study focuses on finding of the amount of heat transfer through a glass substrate that is coated with nanoalumina doped on PMMA matrix. The optical and thermal properties were systematically investigated. The density of heat flow rate, was calculated in the range values (240-260) W/m2 while the optimum values confine between (250-260) W/m2 at temp. (25-35)C^o. The results showed that the thermal insulation of the sample was significantly enhanced at temp. (30-50)C^o. The simulated net heat transfer through window decreased linearly with incr