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.

أن صفة التغير المتسارع في نمط الحياة ولّد مبدأ اللايقين عند إتخاذ القرارات المالية لأي ظاهرة عموماً أو نشاط إقتصادي على وجه الخصوص. وهذا يتطلب الأستعانة بالأدوات الأحصائية كمنهج علمي يساعد في وصفها وتحليلها كمياً ومن ثم التنبؤ بها مستقبلاً كمحاولة لسبر غور اللايقين الذي يكتنف المستقبل كمجهول يتوجس منه الجميع. وقد أصبح متخذ القرار الأستثماري أو صاحب رأس المال وغيرهما من المضاربين والمتعاملين في الاسواق الما

Simple and sensitive kinetic methods are developed for the determination of Paracetamol in pure form and in pharmaceutical preparations. The methods are based on direct reaction (oxidative-coupling reaction) of Paracetamol with o-cresol in the presence of sodium periodate in alkaline medium, to form an intense blue-water-soluble dye that is stable at room temperature, and was followed spectrophotometriclly at λmax= 612 nm. The reaction was studied kinetically by Initial rate and fixed time (at 25 minutes) methods, and the optimization of conditions were fixed. The calibration graphs for drug determination were linear in the concentration ranges (1-7 μg.ml-1) for the initial rate and (1-10 μg.ml-1) for the fixed time methods at 25 min.

It is generally accepted that there are two spectrophotometric techniques for quantifying ceftazidime (CFT) in bulk medications and pharmaceutical formulations.  The methods  are described as simple, sensitive, selective, accurate and efficient techniques. The first method used an alkaline medium to convert ceftazidime to its diazonium salt, which is then combined with the 1-Naphthol (1-NPT) and 2-Naphthol (2-NPT) reagents. The azo dye that was produced brown  and red in color with absorption intensities of ƛmax 585 and 545nm respectively. Beer's law was followed in terms of concentration ranging from  (3-40) µg .ml^-1 For (CFT-1-NPT) and (CFT-2-NPT), the detection limits were 1.0096 and 0.8017 µg.ml^-1, respec

This paper deals with the Magnetohydrodynyamic (Mill)) flow for a viscoclastic fluid of the generalized Oldroyd-B model. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. Exact analytic solutions for the velocity and shear stress fields in terms of the Fox H-function are obtained by using discrete Laplace transform. The effect of different parameter that controlled the motion and shear stress equations are studied through plotting using the MATHEMATICA-8 software.

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

Linguistic studies present a distinguished place among modern human studies, as we find this clear in the scientific research institutions of the developed nations, it is the main pillar in the strengthening of links and consolidation pillars between individuals and groups. It is a language and between people's thoughts, feelings and actions, and has been able to show that language is not only a tool of expression but is closely linked to the intellectual, emotional and social life of these people individuals and groups.
    The derivation is a major step in Arabic in classifying formulas into weights with special morphological values; these are of great importance in sentences and structures that are the domain of the searc

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

Surface modeling utilizing Bezier technique is one of the more important tool in computer aided geometric design (CAD). The aim of this work is to design and implement multi-patches Bezier free-form surface. The technique has an effective contribution in technology domains and in ships, aircrafts, and cars industry, moreover for its wide utilization in making the molds. This work is includes the synthesis of these patches in a method that is allow the participation of these control point for the merge of the patches, and the confluence of patches at similar degree sides due to degree variation per patch.  The model has been implemented to represent the surface. The interior data of the desired surfaces designed by M