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.

This study focused on treatment of real wastewater rejected from leather industry in Al-Nahrawan city in Iraq by Electrocoagulation (EC) process followed by Reverse Osmosis (RO) process. The successive treatment was applied due to high concentration of Cr3+ ions (about 1600 ppm) rejected in wastewater of this industry and for applying EC with moderate power consumption and better results of produced water. In Electrocoagulation process (EC), the effect of NaCl concentration (1.5, 3 g/l), current density (C.D.) (15-25 mA/cm2), electrolysis time (1-2 h), and distance between electrodes (E.D.) (1-2 cm) were examined in a batch cell by implementing Taguchi experimental design. According to the results obtained from multiple regression and signa

Multilateral wells require a sophisticated type of well model to be applied in reservoir simulators to represent them. The model must be able to determine the flow rate of each fluid and the pressure throughout the well. The production rate calculations are very important because they give an indication about some main issues associated with multi-lateral wells such as one branch may produce water or gas before others, no production rate from one branch, and selecting the best location of a new branch for development process easily.                                &nbsp

Cerebral palsy "is one of the diseases that afflict children, and it is a term given to the condition of a child who is exposed to a normal brain injury by accident due to its inability to grow or damage to the cells of the areas responsible for movement and knowledge of strength and balance during the stage of normal development." (116: 1999: 10) Cerebral palsy causes disruption in movement and posture due to damage to brain cells in areas that control and coordinate muscle tone, reflexes, strength, and movement. The degree and location of brain damage varies greatly between people with paralysis, as well as the severity of disability and symptoms, as they fall into severe to very simple, and cerebral palsy is one of the diseases that caus

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

This paper presents a comparison between the electroencephalogram (EEG) channels during scoliosis correction surgeries. Surgeons use many hand tools and electronic devices that directly affect the EEG channels. These noises do not affect the EEG channels uniformly. This research provides a complete system to find the least affected channel by the noise. The presented system consists of five stages: filtering, wavelet decomposing (Level 4), processing the signal bands using four different criteria (mean, energy, entropy and standard deviation), finding the useful channel according to the criteria’s value and, finally, generating a combinational signal from Channels 1 and 2. Experimentally, two channels of EEG data were recorded fro