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, a mathematical model is presented to study the chemisorption of two interacting atoms on solid surface in the presence of laser field. Our mathematical model is based on the occupation numbers formula that depends on the laser field which we derived according to Anderson model for single atom adsorbed on solid surface. Occupation numbers formula and chemisorption energy formula are derived for two interacting atoms (as a diatomic molecule) as they approach to the surface taking into account the correlation effects on each atom and between atoms. This model is characterized by obvious dependence of all relations on the system variables and the laser field characteristics which gives precise description for the molecule –

Mesoporous silica (MPS) nanoparticle was prepared as carriers for drug delivery systems by sol–gel method from sodium silicate as inexpensive precursor of silica and Cocamidopropyl betaine (CABP) as template. The silica particles were characterized by SEM, TEM, AFM, XRD, and N2adsorption–desorption isotherms. The results show that the MPS particle in the nanorange (40-80 nm ) with average diameter equal to 62.15 nm has  rods particle morphology, specific surface area is 1096.122 m²/g, pore volume 0.900 cm³/g, with average pore diameter 2.902 nm, which can serve as efficient carriers for drugs. The adsorption kinetic of Ciprofloxacin (CIP) drug was studied and the data were analyzed and found to match well with

The influence of different thickness (500, 1000, 1500, and 2000) nm on the electrical conductivity and Hall effect measurements have been investigated on the films of copper indium gallium selenide CuIn1-xGaxSe2 (CIGS) for x= 0.6.The films were produced using thermal evaporation technique on glass substrates at R.T from (CIGS) alloy. The electrical conductivity (σ), the activation energies (Ea1, Ea2), Hall mobility and the carrier concentration are investigated and calculated as function of thickness. All films contain two types of transport mechanisms of free carriers, and increases films thickness was fond to increase the electrical cAnductivity whereas the activation energy (Ea) would vary with films thickness. Hall Effect analysis resu

The influence of different thickness (500,750, and 1000) nm on the structure properties electrical conductivity and hall effect measurements have been investigated on the films of copper indium selenide CuInSe2 (CIS) the films were prepared by thermal evaporation technique on glass substrates at RT from compound alloy. The XRD pattern show that the film have poly crystalline structure a, the grain size increasing with as a function the thickness. Electrical conductivity (σ), the activation energies (Ea1,Ea2), hall mobility and the carrier concentration are investigated as function of thickness. All films contain two types of transport mechanisms of free carriers increase films thickness. The electrical conductivity increase with thickness

A nanocrystalline thin films of PbS with different thickness (400, 600)nm have been prepared successfully by chemical bath deposition technique on glass and Si substrates. The structure and morphology of these films were studied by X-ray diffraction and atomic force microscope. It shows that the structure is polycrystalline and the average crystallite size has been measured. The electrical properties of these films have been studied, it was observed that D.C conductivity at room temperature increases with the increase of thickness, From Hall measurements the conductivity for all samples of PbS films is p-type. Carrier's concentration, mobility and drift velocity increases with increasing of thickness. Also p-PbS/n-Si heterojunction has been

This study investigates the characterization and growth dynamics of a Magnetically Stabilized Gliding Arc Discharge (MSGAD) system, generating non-thermal plasma with argon gas under atmospheric pressure and flow rates of 1-5 L/min. The electrical properties and growth patterns concerning gas flow rates and applied voltages were examined utilizing a magnetic field for stability. Using a digital oscilloscope, a correlation between voltage reduction and increased current was uncovered. An algorithm analyzes digital images to compute arc length, area, and volume. Results reveal how gas flow rate and applied voltage directly impact arc growth. Furthermore, the magnetic field's role in guiding and stabilizing the plasma discharge was explored. T

Ceramics type Yttrium oxide with Silicon carbide. were selected to investigate its sintered density, microstructure and electrical properties, after adding V2O5, of 100 nm grain size. Different weight percentages ranging from (0.01,0.02,0.03 and 0.04) were used. Dry milling applied for twelve hours. The pelletized samples were sintered at atmospheric of static air and at sintering temperature 1400 ˚C, for three hours. The crustal structure test shoes the phase which is yttrium silicon carbide Scanning electron microscopy, scan sintered microstructure. Samples after sintering were electrically investigated by measuring its capacitance, dielectric constant and their results showed increasing after added V2O5 particles at the combinat

structural and electrical of CuIn (Sex Te1-x)2