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 relationship between government revenues and the fiscal balance represents a central pillar in the analysis of fiscal sustainability. However, its modeling faces a fundamental challenge in the form of structural uncertainty, which is not captured by point estimates in traditional models such as ARDL, as these models assume structural stability that is inconsistent with the nature of rentier economies. The current study aims to develop a fuzzy framework by constructing a Fuzzy Autoregressive Distributed Lag (FARDL) model. This is achieved through integrating the Autoregressive Distributed Lag (ARDL) approach with fuzzy logic theory, thereby enabling the incorporation of uncertainty into the inherent structure of the economic rela

It is widely accepted that early diagnosis of Alzheimer's disease (AD) makes it possible for patients to gain access to appropriate health care services and would facilitate the development of new therapies. AD starts many years before its clinical manifestations and a biomarker that provides a measure of changes in the brain in this period would be useful for early diagnosis of AD. Given the rapid increase in the number of older people suffering from AD, there is a need for an accurate, low-cost and easy to use biomarkers that could be used to detect AD in its early stages. Potentially, the electroencephalogram (EEG) can play a vital role in this but at present, no reliable EEG biomarker exists for early diagnosis of AD. The gradual s

A system was used to detect injuries in plant leaves by combining machine learning and the principles of image processing. A small agricultural robot was implemented for fine spraying by identifying infected leaves using image processing technology with four different forward speeds (35, 46, 63 and 80 cm/s). The results revealed that increasing the speed of the agricultural robot led to a decrease in the mount of supplements spraying and a detection percentage of infected plants. They also revealed a decrease in the percentage of supplements spraying by 46.89, 52.94, 63.07 and 76% with different forward speeds compared to the traditional method.

TWMS Journal of Applied and Engineering Mathematics | Volume: 16 Issue: 9

This research is an initial attempt to explore the reality of reform and its concept in Islam, and to describe the presence of educational practices in the Arab-Islamic heritage. The importance of this research lies in addressing a number of important issues related to the contemporary Islamic reform system. The research showed the need for authentic educational reform values that draw their reference from the origins of Islam. The research also emphasized the analysis of the reality of education in the Muslim world and the identification of its problems and the search for solutions through a quick and comprehensive look at the diverse contributions of Muslim thinkers to Islamic educational reform thought, and their active role in addressin

The Gulf Cooperation Council (GCC) is the only one in the Arab system, which has been able to formulate a strategic vision with its dimensions and objectives, and that for its great achievements have contributed significantly to the development of the external and internal economic relations of the Gulf Cooperation Council six through the consolidation of economic policies, projects and joint institutions . There is no doubt that the establishment of the Cooperation Council for the Arab Gulf States six, has made security expensive as long as the aspiration to them the leaders and peoples of the region is the adoption of the GCC countries on itself in order to build a self strength ensures cut off the road to all interference in the affai