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.
Praise be to Allah, Lord of the Worlds, and peace and blessings be upon our master Muhammad and his good and pure family. At the end of this research, we summarize some of the most important findings of our research, namely:
Raising a child properly from childhood leads to integrity in the life of the individual society, and if the young raised bad education, this education will affect itself and society negatively, so on parents and government institutions in any country to take care of children, and Islamic countries Specifically to give the child great attention; he is raised on the Koran and watered from its fountains, and armed with a weapon of morality from a young age, and to understand the biography of Mustafa (peace be upon h
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This qualitative study was conducted on eight types of commercial baking yeast which available in local markets to estimate their fermentation activity as affecting the Bread industry and the impact of the salt added to DoughLeavening, The results showed a great variation in the fermentation capacity of yeast samples (their role in swelling the dough), most notably the sample value Y3 and least sample Y7 and reached 80% and 20% respectively, and the value of Leavening by using the two types of yeast with addition of three levels of salt (0 , 1 and 2%) have 20.0 , 19.7 and 15.7 of the sample Y3, compared with 10.5 , 10.3 and 8.8 of the sample Y7 for each of the levels of salt respectively, reflect
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Resumen:
El presente trabajo intenta analizar las características del lenguaje jurídico español a cuya estructura se debe su complejidad. A la vez, damos una descripción detallada de sus rasgos morfosintácticos, léxico-semánticos y estilísticos. En ningún momento, pretendemos fijar unas pautas o normas para la traducción de este lenguaje que requiere unos previos conocimientos jurídicos y cierta preparación para proceder a realizar esta tarea. Nuestra intención es, simplemente, ofrecer al lector árabe una pequeña visión de lo difícil que es comprender los textos legales españoles hasta para los nativos para imaginarse las posibles dificultades a la hora de iniciar a traducirlos.