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.

This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs  in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical exa

In this work, the photoluminescence spectra (PL) of porous silicon (PS) have been modified by adding gold nanoparticles (AuNPs) to PS layer. PS was produced via Photo electro-chemical etching (PECE) method of n-type Si wafer with resistivity of about (10 Ω.cm) and (100) orientation. Laser wavelength of (630 nm) and illumination intensity of about (30 mW/cm2), etching current density of (10mA/cm2), and etching time of (4 min) were used during the etching process. The bare PS before metallic deposition process and porous silicon/gold nanoparticles (PS/AuNPs) structures were investigated by X-Ray Diffraction (XRD), scanning electron microscopy (SEM), and energy dispersive X-Ray (EDX). The photoluminescence spectra were investigated as a fu

During the 1970s, communicative view of language teaching began to be incorporated into syllabus design. The central question for the proponents of this view was: what does the learner want/need to do with the target language? This lead to the emergence of a teaching method (or approach) called communicative language teaching (CLT) during the late 1970s and early 1980s focusing on the functions that must be incorporated into a classroom. According to Brown (2001:43) CLT is a unified but broadly based, theoretically well informed set of tenets about the nature of language and of language learning and teaching. Harmer (2001:84) states that the communicative approach is the name which was given to a set of beliefs which included not only a

 The results of the present study show that the highest elevation point is (912) meters (a.s.l.) inside Wadi Al-Khur basin while the lowest elevation point is (6) meters (a.s.l.) inside Wadi Abu-Talha basin. The biggest catchment area is represented by Wadi Al-Khur (48840 km²) whereas the smallest catchment area is Wadi Taqtaq (1748 km²). The stream direction of all streams trends from South-West towards North-East. The soil available water capacity (AWC) (Moisture Deficit) in the studied area was15 mm. The average annual rainfall was133.11 mm, the average annual temperature was 25.65 C^o, the total depth amount of E Apanwas 3691.85 mm/year, the relative humidity was 40 %, the average annual sunshine is 7.9 hrs., and the

Context has a significant impact on the interpretation of Qur'anic and literary texts, especially in ancient Arabic poetry since that language is no longer considered as a contemporary understandable language. Hence this research is entitled: (the impact of context on the morphological semantics in the Diwan of Abi Al-Aswad Al-Dau’ali) and the morphological meanings indicated by the morphological formula which lack the combination of other contextual clues. The researcher depended on the analytical approach to show the impact of pairing occurring between the contextual elements on determining the morphological meaning.
The most important findings reached at:
1- Context has a great impact in dispelling the possibilities arising fr

Image compression has become one of the most important applications of the image processing field because of the rapid growth in computer power. The corresponding growth in the multimedia market, and the advent of the World Wide Web, which makes the internet easily accessible for everyone. Since the early 1980, digital image sequence processing has been an attractive research area because an image sequence, as acollection of images, may provide much compression than a single image frame. The increased computational complexity and memory space required for image sequence processing, has in fact, becoming more attainable. this research absolute Moment Block Truncation compression technique which is depend on adopting the good points of oth

The - M ultiple mixing ratios of -transitions from levels of 56Fe populated in 56 56 Fe n n Fe ( , )  reactions are calculated by using const. S.T.M. This method has been used in other works [3,7] but with pure transition or with transitions that can be considered as pure transitions، in our work we used This method for mixed  - transitions in addition to pure  - transitions. The experimental angular distribution coefficients a2 was used from previous works [1] in order to calculet - values. It is clear from the results that the - values are in good agreement or consistent, within associated errors, with those reported previously [1]. The discrepancies that occur are due to inaccuracies existing in the expe