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.

The major goal of this research was to use the Euler method to determine the best starting value for eccentricity. Various heights were chosen for satellites that were affected by atmospheric drag. It was explained how to turn the position and velocity components into orbital elements. Also, Euler integration method was explained. The results indicated that the drag is deviated the satellite trajectory from a keplerian orbit. As a result, the Keplerian orbital elements alter throughout time. Additionally, the current analysis showed that Euler method could only be used for low Earth orbits between (100 and 500) km and very small eccentricity (e = 0.001).

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

In this paper the nuclear structure of some of Si-isotopes namely, ^28,32,36,40Si have been studied by calculating the static ground state properties of these isotopes such as charge, proton, neutron and mass densities together with their associated rms radii, neutron skin thicknesses, binding energies, and charge form factors. In performing these investigations, the Skyrme-Hartree-Fock method has been used with different parameterizations; SkM*, S1, S3, SkM, and SkX. The effects of these different parameterizations on the above mentioned properties of the selected isotopes have also been studied so as to specify which of these parameterizations achieves the best agreement between calculated and experimental data. It can be ded

An environmentally friendly technique was used to prepare titanium dioxide@ silver (core shell) (TiO₂@Ag NPs) using chard leaf extract, a natural stabilizer and reductant. A nanocomposite (NCs) of TiO₂@Ag supported by halloysite nanotubes (HNTs), TiO2@Ag/HNT NCs, was prepared under microwave irradiation. The microwave technique is used to accelerate the reaction and enhance the homogeneity of nanoparticle distribution. Spectroscopic and structural analyses were performed on the resulting nanocomposite. X-ray diffraction (XRD) revealed a clear crystalline structure with grain sizes ranging from 7 to 15 nm, with an average of ~11 nm, the transmission electron microscope (TEM) revealed that the size of nanoparticles in the TiO₂@Ag/HNT N

Abstraet

Students dropout from the Education has a negative phenomena on individual and society and even on different aspects of life especially on the economic aspect , Thus our research tries studying and analyzing the relation between the size of dropout and human development level in Iraq and as (research sample) the first decade of this century as a studying period, the study includes the dropout in Secondary schools and depending the formal records as a main source to evaluate the size of this problem in Iraq , which shows an increase in the size of dropout in this period in comparison with the last decades of the twentieth century, this produces a negative effect on human developme