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 analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here. Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical illustrations

تحتل أدوات السياسة المالية (الإنفاقية والإيرادية) مكانة مهمة بين أدوات السياسات الاقتصادية الأخرى لما تتمتع به من تأثيرات اقتصادية واجتماعية على مجمل النشاط الاقتصادي .

     وفي بحثنا هذا سنركز على الآثار الاجتماعية لأدوات السياسة المالية (الإنفاق العام والإيراد العام) لما للتنمية الاجتماعية من أهمية متزايدة في عالمنا اليوم خاصة فيما يتعلق بمقوماتها غير المادية المتمثلة في خدما

The aim of this research is to recognize the tasks undertaken by   the   headmasters   of   intermediate   schools   concerning   time- administration,   in   accordance   to   the   viewpoints   of   the headmasters   of   intermediate   schools   in   the   Administration   of Education   of   Al-Karkh   the   Third.   The   sample   of   this   research consists   of   (60)   headmasters   and &n

Distribution of light intensity in the flat photobioreactor for microalgae cultivation as a step design for production of bio-renewable energy was addressed in the current study. Five sizes of bioreactors with specific distances from the main light source were adopted as independent variables in experiential design model. The results showed that the bioreactor’s location according to the light source, determines the nature of light intensity distribution in the reactor body. However, the cross-section area plays an important role in determining the suitable location of reactor to achieve required light homogeneity. This area could change even the expected response of the light passing through the reactor if Beer-Lambert's law is adopted.

The flexible joint robot manipulators provide various benefits, but also present many control challenges such as nonlinearities, strong coupling, vibration, etc. This paper proposes optimal second order integral sliding mode control (OSOISMC) for a single link flexible joint manipulator to achieve robust and smooth performance. Firstly, the integral sliding mode control is designed, which consists of a linear quadratic regulator (LQR) as a nominal control, and switching control. This control guarantees the system robustness for the entire process. Then, a nonsingularterminal sliding surface is added to give a second order integral sliding mode control (SOISMC), which reduces chartering effect and gives the finite time convergence as well. S

Wind turbine (WT) is now a major renewable energy resource used in the modern world. One of the most significant technologies that use the wind speed (WS) to generate electric power is the horizontal-axis wind turbine. In order to enhance the output power over the rated WS, the blade pitch angle (BPA) is controlled and adjusted in WT. This paper proposes and compares three different controllers of BPA for a 500-kw WT. A PID controller (PIDC), a fuzzy logic controller (FLC) based on Mamdani and Sugeno fuzzy inference systems (FIS), and a hybrid fuzzy-PID controller (HFPIDC) have been applied and compared. Furthermore, Genetic Algorithm (GA) and Particle swarm optimization (PSO) have been applied and compared in order to identify the optimal