The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of fractional differential equations.
This article proposes a new strategy based on a hybrid method that combines the gravitational search algorithm (GSA) with the bat algorithm (BAT) to solve a single-objective optimization problem. It first runs GSA, followed by BAT as the second step. The proposed approach relies on a parameter between 0 and 1 to address the problem of falling into local research because the lack of a local search mechanism increases intensity search, whereas diversity remains high and easily falls into the local optimum. The improvement is equivalent to the speed of the original BAT. Access speed is increased for the best solution. All solutions in the population are updated before the end of the operation of the proposed algorithm. The diversification f
... Show MoreNonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic
... Show MoreRehabilitation robots are widely recognized as vital for restoring motor function in patients with lower-limb impairments. A Modified Fractional-Order Proportional-Integral-Derivative (MFOPID) controller is proposed to improve trajectory tracking of a 2-DoF Lower Limb Rehabilitation Exoskeleton Robot (LLRER). The classical FOPID is augmented with a modified control formulation by which steady-state error is reduced and the transient response is sharpened. Controller gains and fractional orders were tuned offline using a hybrid metaheuristic Improved Elk Herd Optimization hybridized with Grey Wolf and Multi-Verse Optimization algorithms (IElk-GM) so that exploration and exploitation are balanced. Superiority over the classical FOPID
... Show MoreSeparation of Trigonelline, the major alkaloid in fenugreek seeds, is difficult because the extract of these seeds usually contains Trigonelline, choline, mucilage, and steroidal saponins, in addition to some other substances. This study amis to isolate the quaternary ammonium alkaloid (Trigonelline) and choline from fenugreek seeds (Trigonella-foenum graecum L.) which have similar physiochemical properties by modifying of the classical method. Seeds were defatted and then extracted with methanol. The presence of alkaloids was detected by using Mayer's and Dragendorff's reagents. In this work, trigonilline was isolated with traces of choline by subsequent processes of purification using analytical and preparative TLC techniques.
... Show MoreCritical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge
... Show Moreتناولنا في بحثنا أحد اساليب البرمجة الخطية وهي الطريقة المبسطة لتقدير معلمات انموذج الانحدار الخطي عن طريق اختيار دالة الهدف التي تعمل على تقليل الحد الادنى لمجموع الاخطاء الناتجة من تقدير المعلمات بطريقة المربعات الصغرى الاعتيادية ( OLS) حيث سيتم في الطريقة المبسطة ( simplex) فرض قيود على نفس الاخطاء نفسها بهدف تصغيرها الى اقل ما يمكن للحصول على تقديرات افضل لمعلمات انموذج الانحدار الخطي . على اساس ان طريقة المرب
... Show MoreABSTRACT
The research aims to study the effect of the commodity dumping phenomenon that Iraq suffered after 2003 on the consumption pattern of individuals, towards the acquisition of non-essential goods (luxury). To achieve our goal we relied on the questionnaire as a main tool for obtaining information related to the research, and it was distributed on a random sample of consumers in the city of Baghdad with 250 questionnaires. The answers of the research sample were analyzed using the statistical program (SPSS). The percentage weights and the factorial analysis method were used also to arrange the variables that affected on changing consumption patterns. The research reached a set of conclusions:
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