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.

A mathematical model constructed to study the combined effects of the concentration and the thermodiffusion on the nanoparticles of a Jeffrey fluid with a magnetic field effect the process of containing waves in a three-dimensional rectangular porous medium canal. Using the HPM to solve the nonlinear and coupled partial differential equations. Numerical results were obtained for temperature distribution, nanoparticles concentration, velocity, pressure rise, pressure gradient, friction force and stream function. Through the graphs, it was found that the velocity of fluid rises with the increase of a mean rate of volume flow and a magnetic parameter, while the velocity goes down with the increasing a Darcy number and lateral walls. Also, t

The effects of using aqueous nanofluids containing covalently functionalized graphene nanoplatelets with triethanolamine (TEA-GNPs) as novel working fluids on the thermal performance of a flat-plate solar collector (FPSC) have been investigated. Water-based nanofluids with weight concentrations of 0.025%, 0.05%, 0.075%, and 0.1% of TEA-GNPs with specific surface areas of 300, 500, and 750 m2/g were prepared. An experimental setup was designed and built and a simulation program using MATLAB was developed. Experimental tests were performed using inlet fluid temperatures of 30, 40, and 50 °C; flow rates of 0.6, 1.0, and 1.4 kg/min; and heat flux intensities of 600, 800, and 1000 W/m2. The FPSC’s efficiency increased as the flow rate and hea

     The bubble columns are widely used as a two or three phase reactor in industrial chemical process such as absorption, biochemical reactions, coal liquefaction, etc. To design such a column, two main parameters should be taken in consideration, the gas hold-up (), and the liquid phase mass transfer coefficient K_La. The study includes the effect of gas velocity and the addition of alcohols on gas hold-up and mass transfer coefficient in bubble column with draught tube when the length of the column is 1.5m and the ratio of the draught tube diameter to the column diameter equals 0.5 and the air dispersion into the base of the draught tube using a multi hole tuyere is equivalent to a diameter of 0.15 mm and

Potential health and environmental effects of nanoparticles need to be thoroughly assessed before their widespread commercialization. The present investigation was planned with the aims to determine the effects of gold nanoparticles (GNPs) on blast (BI) and mitotic (MI) indices of cultured lymphocytes. The results revealed that BI (50.3±2.3, 30.2±1.9, 10.5±0.7 and 0.0%, respectively) and MI (70.1±2.9, 20.4±1.1, 5.3±0.1 and 0.0%, respectively) showed a gradual decreased percentage as the concentration of GNPs was increased from 0.085 to 0.66 µg/mL, and the difference was significant compared to control culture (81.6±2.5 and 90.2±3.7%, respectively). A maximum inhibition of BI and MI was occurred at the concentration 0.66 µg/mL. In

In this work, CdS/TiO2 nanotubes composite nanofilms were successfully synthesized via electrodeposition technique. TiO2 titania nanotube arrays (NTAs) are commonly used in photoelectrochemical cells as the photoelectrode due to their high surface area, excellent charge transfer between interfaces and fewer interfacial grain boundaries. The anodization technique of titanium foil was used to prepare TiO2 NTAs photoelectrode. The concentration of CdCl2 played an important role in the formation of CdS nanoparticles. Field emission scanning electron microscopy (FESEM) shows that the CdS nanoparticles were well deposited onto the outer and inner of nanotube at 40 mM of CdCl2. X-ray diffraction (XRD) and energy dispersive X-ray (EDX) analyses wer