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 God, who said: {And establish prayer and pay zakat and lend to God a good loan, and whatever good you put forward for yourselves you will find with God. It is better and greater in reward. Ask forgiveness of God. Indeed, God is Forgiving, Most Merciful. May blessings and peace be upon Muhammad, the servant of God, and His Messenger, may God bless him and grant him peace, who said: “Islam is built on five Testifying that there is no god but God and that Muhammad is the Messenger of God, establishing prayer, paying zakat, Hajj, and fasting Ramadan” ().
Now that follows: Islamic law aims to make man happy in this world and the afterlife, starting with faith in God Almighty until the end of the legal obligations. This is
The study aims to demonstrate the importance of instructional methods in teaching Arabic language as a second language or teaching the Arabic language to non-native speakers. The study is in line with the tremendous development in the field of knowledge, especially in the field of technology and communication, and the emergence of many electronic media in education in general and language teaching in particular. It employs an image in teaching vocabulary and presenting the experience of the Arabic Language Institute for Non-Speakers-King Abdul-Aziz University. The study follows the descriptive approach to solve the problem represented by the lack of interest in the educational methods when teaching Arabic as a second language. Accordingl
... Show MoreBACKGROUND: Acute appendicitis (AA) remains a complex case even for experienced surgeons. Rate of negative appendectomy is 5–40% and delayed intervention result in perforated appendicitis in 5–30% of cases. AIM: The aim of the study was to evaluate NPT as a marker for the diagnosis of AA concerning its severity. And compare the diagnostic value of it with the ALV scoring system. METHODS: One hundred twenty patients presented with signs and symptoms of AA and underwent appendectomy, only 84 patients proved to be AA by histopathological examination, were included in the study. Blood samples for neopterin (NPT) estimation and Alvarado (ALV) score was calculated. Control group consists of 45 healthy individual. RESULTS: NPT levels were s
... Show MoreAntibiotic resistance has been a growing worldwide public health issue. The World Health Organization (WHO) has stated that the search for new antibiotics is slow, while antibiotic resistance is growing. WHO has also declared that antibiotic resistance is one of the top 10 global public health threats facing humanity in the 21st century. Therefore, this review discusses the potential of metal-based drugs as antibacterial agents from the period of the early 2000s to date. The review reveals that a lot of preliminary work has been done to assess these as potential drugs. However, their mode of action is faintly described. Furthermore, a few examples of metal-based drugs assessed for their modes of action are described. These compounds are ide
... Show MoreBackground: Chronic kidney disease is a gradual loss of kidney function with diabetes and hypertension as the leading cause. Chronic kidney disease is one of these systemic diseases that can affect salivary contents. Aims: This study aimed to assess salivary immunoglobulin A, interleukin-6 and C- reactive protein in chronic kidney disease patients on hemodialysis and those on conservative treatment in comparison with control subjects. Materials and methods: Ninety subjects were included in this study divided into three groups: 30 patients with chronic kidney disease on hemodialysis for at least 6 months ago; 30 patients with chronic kidney disease on conservative treatment and 30 healthy control subjects. Secretory immunoglobulin A, inte
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