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.

In this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami

Progression in Computer networks and emerging of new technologies in this field helps to find out new protocols and frameworks that provides new computer network-based services. E-government services, a modernized version of conventional government, are created through the steady evolution of technology in addition to the growing need of societies for numerous services. Government services are deeply related to citizens’ daily lives; therefore, it is important to evolve with technological developments—it is necessary to move from the traditional methods of managing government work to cutting-edge technical approaches that improve the effectiveness of government systems for providing services to citizens. Blockchain technology is amon

Nutrient enrichment of Sawa lake water was made using different nitrogen and phosphorus concentrations during autumn and spring at three stations. Different concentrations of nitrogen, phosphorus and N: P ratios were used to test variations in phytoplankton population dynamics. Nitrogen at a concentration of 25 µmole.l-1 and N: P ratio of 10:1 gave highest phytoplankton cell number at all stations and seasons. A total of 64 algal taxa dominated by Bacillariophyceae followed by Cyanophyceae and Chlorophyceae were identified. The values of Shannon index of diversity were more than one in the studied stations.

Phytoplankton community is a model for of monitoring  aquatic systems and interpreting the environmental change in aquatic systems. The present study aimed to forecast environmental parameters that drive the change of phytoplankton community structure in the lake. The present study was carried out in Baghdad Tourist Island Lake (BTIL) for the period From October 2021 to May 2022. The study included the quality and quantity of phytoplankton, moreover, the highest and lowest value of the physical and chemical parameters were (Water temperature (13-30 °C), Light penetration (94-275cm), electric conductivity (837-1128 µS/cm), salinity (0.5-0.7 ‰), pH (7-8.2), total alkalinity (126-226 mg CaCO3/L), total Hardness (297-395 mg CaCO3/L

  This paper deals  the prediction of the process of  random spatial data of two properties, the first is called  Primary variables  and the second is called secondary  variables ,   the method  that were used in the  prediction process for this type  of data is technique Co-kriging  , the method is usually used when the number of primary variables  meant to predict for one of its elements is measured in a particular location a few (because of the cost or difficulty of obtaining them) compare with secondary variable which is the number of elements  are available and  highly correlated with primary variables, as was the&nbs

In light of crises, the need for efficient and flexible public administrations to make quick and decisive decisions, also institutions capable of directing the internal elements and components of them and adapting them to the requirements of rapid change due to crises and disasters, which led to scarce resources becoming scarcer and economic, political and social problems becomes more prominent. For the majority of developing countries, including Iraq, the increasing need for the importance of moving towards enhancing the efficiency of the performance of public institutions while trying to predict their future, can only be achieved. Through solid mechanisms and principles of governance that enhance the ability of institutions and make them