This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended approach is applicable and accurate for solving such kinds of problems.
Abstract
The traffic jams taking place in the cities of the Republic of Iraq in general and the province of Diwaniyah especially, causes return to the large numbers of the modern vehicles that have been imported in the last ten years and the lack of omission for old vehicles in the province, resulting in the accumulation of a large number of vehicles that exceed the capacity of the city's streets, all these reasons combined led to traffic congestion clear at the time of the beginning of work in the morning, So researchers chose local area network of the main roads of the province of Diwaniyah, which is considered the most important in terms of traffic congestion, it was identified fuzzy numbers for
... Show MoreIn this research ,Undoped Nio and 1%Li doped Nio thin films were deposited utilizing chemical spray pyrolysis on the glass substrates heated (450C). The effects of non-thermal plasma on the structural and optical properties were studied. XRD measurement shows that Nio and Nio:1%Li films were found to be polycrystalline and have cubic structure with a preferred orientation (111). Decreased crystal size after exposure especially at (7) sec. AFM data indicate that the surface roughness average and (RMS) values of the prepared doped films are increasing after exposure to plasma, the transmittance increases after doped samples exposure to plasma, it was found that the energy gap value decreased when doped samples exposure to plasma, also, thickn
... Show MoreIn this work, ZnS thin films have been deposited by developed laser deposition technique on glass substrates at room temperature. After deposition process, the films were annealed at different temperatures (200ºC , 300 ºC and 400ºC ) using thermal furnace.The developed technique was used to obtain homogeneous thin films of ZnS depending on vaporization of this semiconductor material by continuous CO2 laser with a simple fan to ensure obtaining homogeneous films. ZnS thin films were annealed at temperature 200ºC, 300 ºC and 400ºC for (20) minute in vacuum environment. Optical properties of ZnS thin film such as absorbance, transmittance, reflectance, optical band gap, refractive index extinction coefficient and absorption coefficien
... Show MoreIn this work, multilayer nanostructures were prepared from two metal oxide thin films by dc reactive magnetron sputtering technique. These metal oxide were nickel oxide (NiO) and titanium dioxide (TiO2). The prepared nanostructures showed high structural purity as confirmed by the spectroscopic and structural characterization tests, mainly FTIR, XRD and EDX. This feature may be attributed to the fine control of operation parameters of dc reactive magnetron sputtering system as well as the preparation conditions using the same system. The nanostructures prepared in this work can be successfully used for the fabrication of nanodevices for photonics and optoelectronics requiring highly-pure nanomaterials.
Pulsed laser deposition (PLD) technique was applied to prepared Chromium oxide (Cr2O3) nanostructure doped with Titanium oxide (TiO2) thin films at different concentration ratios 3,5,7 and 9 wt % of TiO2. The effect of TiO2 dopant on the average size of crystallite of the synthesized nanostructures was examined by X-ray diffraction. The morphological properties were discussed using atomic force microscopy(AFM). Observed optical band gap value ranged from 2.68 eV to 2.55 eV by ultraviolet visible(UV-Vis.) absorption spectroscopy with longer wave length shifted in comparison with that of the bulk Cr2O3 ~3eV. This indicated that the synthesized samples a
... Show MoreThe polymer was used to inhibit the corrosion of copper metal in salt media in different concentrations at room temperature using potentiometric polarization measurement. The polymer was prepared by mixing (0.1 M) 4-Hydroxy aniline (C6H7NO) with (0.25M) of ammonium persulfate as the initiator using the electro-deposition technique. The polymer’s results showed that copper in (3.5%) NaCl had good corrosion resistance. The findings demonstrate that the %IE for polymer-induced copper corrosion is 89.32% at 10 ppm concentration as a result of the 4-hydroxy aniline polymer’s adsorption from salt solution on the surface of copper metal. The numbers from the polarization method and the acquired standard data agree well. The coated copper by po
... Show MoreIn this work, pure and Ag-doped nickel oxide (NiO) thin films were deposited on glass substrates with different dopant concentrations (0.1, 0.2, 0.3 and 0.4 wt.%) by pulsed-laser deposition (PLD) technique at room temperature. These films were annealed at temperature of 450 °C. The structural and optical properties of the prepared thin films were studied. It was found that annealing process has lead to increase the transmittance of the deposited films. Also, the transmittance was found to increase with doping concentration of silver in the deposited NiO films. The optical energy gap was decreased from 3.5 to 3.2 eV as the doping concentration was increased to 0.4 %.
The polymer was used to inhibit the corrosion of copper metal in salt media in di erent concentrations at room temperature using potentiometric polarization measurement. The polymer was prepared by mixing (0.1 M) 4-Hydroxy aniline (C6H7NO) with (0.25M) of ammonium persulfate as the initiator using the electro-deposition technique. The polymer’s results showed that copper in (3.5%) NaCl had good corrosion resistance. The ndings demonstrate that the %IE for polymer-induced copper corrosion is 89.32% at 10 ppm concentration as a result of the 4-hydroxy aniline polymer’s adsorption from salt solution on the surface of copper metal. The numbers from the polarization method and the acquired standard data agree well. The coated copper by poly
... Show MoreCr2O3 thin films have been prepared by spray pyrolysis on a glass substrate. Absorbance and transmittance spectra were recorded in the wavelength range (300-900) nm before and after annealing. The effects of annealing temperature on absorption coefficient, refractive index, extinction coefficient, real and imaginary parts of dielectric constant and optical conductivity were expected. It was found that all these parameters increase as the annealing temperature increased to 550°C.