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.
Contemporary life is racing against time in its temptations and variables, and it has become shaped and changed in an amazing way in its various aspects and fields. This was facilitated by intellectual and scientific communication between civilizations, and the rapid progression in successive inventions and discoveries in the fields of science and arts of knowledge. This contributed to a great economic and commercial renaissance. Then, these economic developments entered the world into a very strong competition, which forced producers to calculate all production costs, to reach the highest profits by reducing the price of the produced commodity on the one hand, and achieving quality in appearance (especially) on the other hand. Since the ma
... Show MoreThe 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
... Show MoreIn the present study, five derivatives have been designed to be synthesized as possible mutual prodrugs for 5-Fluorouracil (5-FU) and non steroidal anti-inflammatory drugs (NSAIDs) to selectively deliver the drugs into the cancer cells. The synthesis of the target compounds were accomplished following multistep reaction procedures, the chemical reaction followed up and the purity of the products were checked by TLC. The structure of the final compounds and their intermediates were confirmed by their melting points, infrared spectroscopy and elemental microanalysis, the hydrolysis of compound III was studied using HPLC technique. According to the results mentioned above, compounds (I−V) can be good candidates as possible mutual prod
... Show MoreThis work studied the electrical and thermal surface conductivity enhancement of polymethylmethacrylate (PMMA) clouded by double-walled carbon nanotubes (DWCNTs) and multi-walled carbon nanotube (MWCNTs) by using pulsed Nd:YAG laser. Variable input factors are considered as the laser energy (or the relevant power), pulse duration and pulse repetition rate. Results indicated that the DWCNTs increased the PMMA’s surface electrical conductivity from 10-15 S/m to 0.813×103 S/m while the MWCNTs raised it to 0.14×103 S/m. Hence, the DWCNTs achieved an increase of almost 6 times than that for the MWCNTs. Moreover, the former increased the thermal conductivity of the surface by 8 times and the later by 5 times.
In this paper, an intelligent tracking control system of both single- and double-axis Piezoelectric Micropositioner stage is designed using Genetic Algorithms (GAs) method for the optimal Proportional-Integral-Derivative (PID) controller tuning parameters. The (GA)-based PID control design approach is a methodology to tune a (PID) controller in an optimal control sense with respect to specified objective function. By using the (GA)-based PID control approach, the high-performance trajectory tracking responses of the Piezoelectric Micropositioner stage can be obtained. The (GA) code was built and the simulation results were obtained using MATLAB environment. The Piezoelectric Micropositioner simulation model with th
... Show MoreIn this paper the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control
... Show Moreتم تحضير ثلاث معقدات جديدة Ni (II)و Cu (II) و Zn (II) باستخدام الليكند المحضر الجديد من تفاعل حامض مالونيك ثنائي هيدرازايد مع 2-بيريدين كربوكسالديهايد. حيث شخصت المعقدات لمحضرة وكذلك الليكند باستخدام تقنيات مختلفة مثل FT-IR و UV-Vis و Mass و 1H-NMR و 13C-NMR وتحليل العناصر CHN و تقدير محتوى الكلور والموصلية المولارية والحساسية المغناطيسية والامتصاص الذري لتشخيص هذه المركبات. لكل معقد محضر جديد من النيكل والنحاس والزنك ، كشفت نتائج ا
... Show MoreBiological activity of the carotenoids which are produced fromchemically-mutaed local isolate of Rhodotorula mucilaginosawas studied. The results showed variation of inhibition activity of caritenoids against different types of pathogenic bacteria include, Staph aureus, E. coli, B. subtilis and Salmo. typh., the number declined from 2×107cell/ml to 2×104, 5×104, 2×105, 9×105 cell/ml respectively after 24hour. The produced carotenoids from alocal mutant Rhodotorula mucilaginosa revealed an antioxidant activity as free radical removal of 85.6%. Carotinoides revealed a highest stability in petroleum ether solvent for 30 days at room temperature. It found that the pigment was more stability in sesame oil compared with sun flower and coc
... Show More