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 current study aims to develop a teaching design in accordance with cluster thinking strategies and explore the effect of this teaching design on students’ achievement in science. To this end, the null hypothesis was adopted: there is no statistically significant difference at the level of (0, 05) between experimental group who adopted the teaching design in learning science and control group who follow the traditional method in learning the same subject. To test the null hypothesis, total of (74) students from Al-Alaama Hussain Mahfooth intermediate school were selected intentionally for the academic year 2016-2017. The sample divided into two equal groups when all the variables (age, prior achievement of science,

Tourism is one of the most important sources of income of economic key countries in the world so are imports of tourism for some countries a source of income is not significant of the total revenues of States. Making those countries, and those countries a destination for visitors, and here should be interest in the Wealth and cultural heritage that distinguishes Islamic countries in general, and Iraq in particular, must be placed specialist studies in all areas for the development of this area of tourism, especially religious tourism to achieve a desired and desired of such research.It is the most important ways to develop tourism in general and religious tourism is of particular publications, advertising, and is important for us in this

Sensitive information of any multimedia must be encrypted before transmission. The dual chaotic algorithm is a good option to encrypt sensitive information by using different parameters and different initial conditions for two chaotic maps. A dual chaotic framework creates a complex chaotic trajectory to prevent the illegal use of information from eavesdroppers. Limited precisions of a single chaotic map cause a degradation in the dynamical behavior of the communication system. To overcome this degradation issue in, a novel form of dual chaos map algorithm is analyzed. To maintain the stability of the dynamical system, the Lyapunov Exponent (LE) is determined for the single and dual maps. In this paper, the LE of the single and dual maps

The research aims to know the effectiveness of a training program based on multiple intelligence theory in developing literary thinking among students of the Arabic Language Department at Ibn Rushd School of Humanities and to achieve the goal of research, the Safaris Research Institute, and the research community of Arabic language students in the Faculty of Education the third section of Arabic Language: The research sample consists of (71) students. Divided into (35) students in the experimental group and (36) students in the control group, the researcher balanced between the two groups with variables (intelligence, testing of tribal literary thinking, and time age in months), and after using the T-test for two independent samples, the

Simplifying formulas that are used for calculations and design are the aim of researchers. For present work, the approach to distinguish the flow under sluice gate was conducted in a laboratory. The extensive experimental program was done to collect fifty-four data points for both free and submerged flow conditions. The data included different discharges, gate openings, flow depths at upstream as well as the flow depths represent a tail water and at a contracted section for downstream. The collected data are analyzed according to a problematic that may encounter in the field, to present a more straightforward (but with acceptable accurate) practical features equations and charts. Based on the proposed formulas, five meth