In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

Nanostructure of chromium oxide (Cr₂O₃-NPs) with rhombohedral structure were successfully prepared by spray pyrolysis technique using Aqueous solution of Chromium (III) chloride CrCl₃ as solution. The films were deposited on glass substrates heated to 450°C using X-ray diffraction (XRD) shows the nature of polycrystalline samples. The calculated lattice constant value for the grown Cr₂O₃ nanostructures is a = b = 4.959 Å & c = 13.594 Å and the average crystallize size (46.3-55.6) nm calculated from diffraction peaks, Spectral analysis revealed FTIR peak characteristic vibrations of Cr-O Extended and Two sharp peaks present at 630 and 578 cm-1 attributed to Cr-O “stretching

Providing Iraqi students with proficiency in English is the ultimate goal of the educational system which is a way of getting knowledge in the fields of arts, sciences, transferring knowledge and sciences to other communities. Therefore, conducting such a type of study is very important because the contents of English textbooks have a huge influence on learning of the students. Once the content of English textbooks contain errors as the correct one, this will effect on his/her learning. The present study is an attempt to evaluate the new course entitled “English for Iraq” for fifth grade students for secondary schools, by Olivia Johnston and Mark Farell. It aims to answer eleven questions relating to the following domains: strength, obj

An integrated GIS-VBA (Geographical Information System – Visual Basic for Application), model is developed for selecting an optimum water harvesting dam location among an available locations in a watershed. The proposed model allows quick and precise estimation of an adopted weighted objective function for each selected location. In addition to that for each location, a different dam height is used as a nominee for optimum selection. The VBA model includes an optimization model with a weighted objective function that includes beneficiary items (positive) , such as the available storage , the dam height allowed by the site as an indicator for the potential of hydroelectric power generation , the rainfall rate as a source of water . In a

The issue of increasing the range covered by a wireless sensor network with restricted sensors is addressed utilizing improved CS employing the PSO algorithm and opposition-based learning (ICS-PSO-OBL). At first, the iteration is carried out by updating the old solution dimension by dimension to achieve independent updating across the dimensions in the high-dimensional optimization problem. The PSO operator is then incorporated to lessen the preference random walk stage's imbalance between exploration and exploitation ability. Exceptional individuals are selected from the population using OBL to boost the chance of finding the optimal solution based on the fitness value. The ICS-PSO-OBL is used to maximize coverage in WSN by converting r

In this study, sulfur was removed from imitation oil using oxidative desulfurization process. Silicoaluminophosphate (SAPO-11) was prepared using the hydrothermal method with a concentration of carbon nanotubes (CNT) of 0% and 7.5% at 190 °C crystallization temperature. The final molar composition of the as-prepared SAPO-11 was Al2O3: 0.93P2O5: 0.414SiO2. 4% MO/SAPO-11 was prepared using impregnation methods. The produced SAPO-11 was described using X-ray diffraction (XRD) and Brunauer-Emmet-Teller (N2 adsorption–desorption isotherms). It was found that the addition of CNT increased the crystallinity of SAPO-11. The results showed that the surface area of SAPO-11 containing 7.5% CNT was 179.54 m2/g, and the pore volume was 0.31

Decolorization of red azo dye (Cibacron Red FN-R) from synthetic wastewater has been investigated as a function of solar advanced oxidation process. The photocatalytic activity using ZnO as a photocatalysis has been estimated. Different parameters affected the removal efficiency, including pH of the solution, initial dye concentration and H2O2 concentration were evaluated to find out the optimum value of these parameters. The results proved that the optimal pH value was 8 and the most efficient H2O2 concentration was 100mg/L. Toxicity reduction percent for effluent solution was also monitored to assess the degradation process. This treatment method was able to strongly reduce the color and toxicity of reactive red dye-238 to about (99 an