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

The influence of an aortic aneurysm on blood flow waveforms is well established, but how to exploit this link for diagnostic purposes still remains challenging. This work uses a combination of experimental and computational modelling to study how aneurysms of various size affect the waveforms. Experimental studies are carried out on fusiform-type aneurysm models, and a comparison of results with those from a one-dimensional fluid–structure interaction model shows close agreement. Further mathematical analysis of these results allows the definition of several indicators that characterize the impact of an aneurysm on waveforms. These indicators are then further studied in a computational model of a systemic blood flow network. This demonstr

In this research, the results of the Integral breadth method were used to analyze the X-ray lines to determine the crystallite size and lattice strain of the zirconium oxide nanoparticles and the value of the crystal size was equal to (8.2nm) and the lattice strain (0.001955), and then the results were compared with three other methods, which are the Scherer and Scherer dynamical diffraction theory and two formulas of the Scherer and Wilson method.the results were as followsScherer crystallite size(7.4nm)and lattice strain(0.011968),Schererdynamic method crystallite size(7.5 nm),Scherrer and Wilson methodcrystallite size( 8.5nm) and lattice strain( 0.001919).And using another formula for Schearer and Wilson methodwe obtain the size of the c

A sensitive and selective method have been developed for the determination of palladium (II)and platinum (II) . A new reagent and two complexes have been prepared in ethanolic solutions .The method is based on the chelation of metal ions with 4-(4?- pyrazolon azo) resorcinol (APAR) to form intense color soluble products, that are stable and have a maximum absorption at 595 nm and at 463 nm and ?max of 1.11×10 4 and.1.35 ×104 Lmole-1cm-1 for Pd(II) Pt(II) respectively. A linear correlation of (1.4 – 0.2) and (3.2 -0.4 ) ppm for pd(II) pt(II) respectively .The stability constants , relative errors , a relative standard deviations for Pd(II) and Pt(II) were 0.40×105 , 0.4×104 L mol-1 ,0.34 - 0.21% and 2.4 – 0.91% respectively.