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.

Accurate predictive tools for VLE calculation are always needed. A new method is introduced for VLE calculation which is very simple to apply with very good results compared with previously used methods. It does not need any physical property except each binary system need tow constants only. Also, this method can be applied to calculate VLE data for any binary system at any polarity or from any group family. But the system binary should not confirm an azeotrope. This new method is expanding in application to cover a range of temperature. This expansion does not need anything except the application of the new proposed form with the system of two constants. This method with its development is applied to 56 binary mixtures with 1120 equili

The aim of the research is to:. Preparation and implementation of special educational units using multimedia to learn the skill of scrolling from below. 2 to recognize the impact of the use of multimedia in learning the skill of scrolling from below. 3 to identify the differences between the tests after the two groups research in learning the skill of passing from the bottom volleyball. The research represented the students of the first stage and the sample of the research was drawn randomly and the number of (50) students were divided into two experimental and control groups and each group (25) students were used standardized tests and conducting pre-tests and the implementation of the main exp

LandSat Satellite ETM+ image have been analyzed to detect the different depths of regions inside the Tigris river in order to detect the regions that need to remove sedimentation in Baghdad in Iraq Country. The scene consisted of six bands (without the thermal band), It was captured in March ٢٠٠١. The variance in depth is determined by applying the rationing technique on the bands ٣ and ٥. GIS ٩. ١ program is used to apply the rationing technique and determined the results.

One of the most significant environmental issues facing the planet today is air pollution. Due to development in industry and population density, air pollution has lately gotten worse. Like many developing nations, Iraq suffers from air pollution, particularly in its urban areas with heavy industry. Our research was carried out in Baghdad's Al-Nahrawan neighbourhood. Recently, ground surveys and remote sensing were used to study the monitoring of air pollution. In order to extract different gaseous and particle data, Earth Data source, Google Earth Engine (GEE), and Geographic Information Systems (GIS) software were all employed. The findings demonstrated that there is a significant positive connection between data collected by ground-ba

Ubikh is one of the most important tribes of the Northwest Caucasus and has a long history. Naturally, rebukes are an integral part of the Caucasus region. Their people were able to confront the Russian invasion of their lands like the rest of the Caucasus tribes to defend their existence, freedom and the right to build their independent state, but they were not able to resist the great Russian military progress they achieved on all sides. For the territory that belonged to Persia and the Ottoman Empire and ended the resistance of the Meridian movement in the Northeast Caucasus, the Russians left only the weak resistance of the tribes of the Northwest Caucasus led by the rebuke after Russia managed to eliminate all resistance movements i