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 avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels

Peripheral neuropathy represents one of the common diabetic complications in patients with diabetes mellitus type 2 (DMT2). Peripheral neuropathy affects the feet, legs, hands, and arms. It was found that one-third to one-half of diabetics have peripheral neuropathy. The current study aimed to evaluate the level of visfatin in diabetic patient groups with or without peripheral neuropathy in comparison with healthy subjects to knowledge whether visfatin can be applied as a predictor factor for this type of disease complication. The study included 120 males and females ranging in age from 40 to 97 years old. (40 patients with type 2 diabetes, 40 patients with diabetic peripheral neuropathy, and 40 healthy people served as the control group

Steel–concrete–steel (SCS) structural systems have economic and structural advantages over traditional reinforced concrete; thus, they have been widely used. The performance of concrete made from recycled rubber aggregate from scrap tires has been evaluated since the early 1990s. The use of rubberized concrete in structural construction remains necessary because of its high impact resistance, increases ductility, and produces a lightweight concrete; therefore, it adds such important properties to SCS members. In this research, the use of different concrete core materials in SCS was examined. Twelve SCS specimens were subjected to push-out monotonic loading for inspecting their mechanical performance. One specimen was constructed from co

Infertility is one of the types of diseases that occur in the reproductive system. Obesity is a state that can be occurred due to excessive fats, the progression in obesity stage results in a change in adipose tissue and the development of chronic inflammation, endocrine glands disorders and women’s reproductive system, and also increase the infection with covid-19. The study aimed to investigate the effect of the obesity, lipid-profile, and IL-6 on hormones-dysregulation in infertile-women with COVID-19 complications. The current study included 70 samples: 50 infertility-women-with-covid-19-infected, 20 healthy-women/control, the ages of both patients and healthy subjects were selected within the range 18-34 years. Levels of FBS, LH,