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 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 study showed that all extracts (aqueous, ethanolic and acetonic) of the leaves of Eucalyptus and Myrtus plants had a inhibitory effect on the growth of all types of yeasts studied, acetone extract recorded the highest inhibition of yeastat 100ppm concentration,The inhibition was 35mm, 34mm, 24mm and 20mm for Candida parapsilosis, Candida glabrata, Candida tropicalis and Candida albicans respectively, The experiments above showed the least significant differences at 0.05 level.The results ofE. Cammldulensis ethanolic tincture analysis has shown the presence of 44 biologically active substances. The main Eucalyptus leaves component was: 2-Bicyclo (2-2.1) heptanol (12.37%), Ledol (8.23%),1,2,4- Benzenetriol (8.45%) and that contain spathul

Flexible pavements are subjected to three main distress types: fatigue crack, thermal crack, and permanent deformation. Under severe climate conditions, thermal cracking particularly contributes largely to a considerable scale of premature deterioration of pavement infrastructure worldwide. This challenge is especially relevant for Europe, as weather conditions vary significantly throughout the year. Hydrated lime (HL) has been recognized as an effective additive to improve the mechanical properties of asphalt concrete for pavement applications. Previous research has found that a replacement of conventional limestone dust filler using hydrated lime at 2.5% of the total weight of aggregates generated an optimum improvement in the mec

The nucleon momentum distributions (NMD) and elastic electron scattering form factors of the ground state for some 1f-2p-shell nuclei, such as ⁵⁸Ni, ⁶⁰Ni, ⁶²Ni, and ⁶⁴Ni
isotopes have been calculated in the framework of the coherent fluctuation model (CFM) and expressed in terms of the weight function lf(x)l² . The weight function (fluctuation function) has been related to the nucleon density distribution (NDD) of the nuclei and determined from the theory and experiment. The NDD is derived from a simple method based on the use of the single particle wave functions of the harmonic oscillator potential and the occupation numbers of the states. The feature of the l