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.
This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.
In This paper, we have been approximated Grűnwald-Letnikov Derivative of a function having m continuous derivatives by Bernstein Chlodowsky polynomials with proving its best approximation. As well as we have been solved Bagley-Torvik equation and Fokker–Planck equation where the derivative is in Grűnwald-Letnikov sense.
In this work, metal oxide nanostructures, mainly copper oxide (CuO), nickel oxide (NiO), titanium dioxide (TiO2), and multilayer structure, were synthesized by the DC reactive magnetron sputtering technique. The effect of deposition time on the spectroscopic characteristics, as well as on the nanoparticle size, was determined. A long deposition time allows more metal atoms sputtered from the target to bond to oxygen atoms and form CuO, NiO, or TiO2 molecules deposited as thin films on glass substrates. The structural characteristics of the final samples showed high structural purity as no other compounds than CuO, NiO, and TiO2 were found in the final samples. Also, the prepared multilayer structures did not show new compounds other than th
... Show MoreWater pollution as a result of contamination with dye-contaminating effluents is a severe issue for water reservoirs, which instigated the study of biodegradation of Reactive Red 195 and Reactive Blue dyes by E. coli and Bacillus sp. The effects of occupation time, solution pH, initial dyes concentrations, biomass loading, and temperature were investigated via batch-system experiments by using the Design of Experiment (DOE) for 2 levels and 5 factors response surface methodology (RSM). The operational conditions used for these factors were optimized using quadratic techniques by reducing the number of experiments. The results revealed that the two types of bacteria had a powerful effect on biodegradable dyes. The regression analysis reveale
... 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.
Cu X Zn1-XO films with different x content have been prepared by
pulse laser deposition technique at room temperatures (RT) and
different annealing temperatures (373 and 473) K. The effect of x
content of Cu (0, 0.2, 0.4, 0.6, 0.8) wt.% on morphology and
electrical properties of CuXZn1-XO thin films have been studied.
AFM measurements showed that the average grain size values for
CuXZn1-xO thin films at RT and different annealing temperatures
(373, 473) K decreases, while the average Roughness values increase
with increasing x content. The D.C conductivity for all films
increases as the x content increase and decreases with increasing the
annealing temperatures. Hall measurements showed that there are
two
In 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 MoreCarbon nanotubes (CNTs) were synthesized via liquefied petroleum gas (LPG) as precursor using flame fragments deposition (FFD) technique. In vitro, biological activates of carbon nanotubes (CNTs) synthesized by FFD technique were investigated. The physiochemical characterizations of synthesized CNTs are similar to other synthesized CNTs and to the standard sample. Pharmaceutical application of synthesized CNTs was studied via conjugation and adsorption with different types of medicines as promote groups. The conjugation of CNTs was performed by adsorption the drugs such as sulfamethoxazole (SMX) and trimethoprim (TMP) on CNTs depending on physical properties of both bonded parts. The synthesized CNTs almost have the same performance in a
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