This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

     The variational iteration method is used to deal with linear and nonlinear differential equations. The main characteristics of the method lie in its flexibility and ability to accurately and easily solve nonlinear equations. In this work, a general framework is presented for a variational iteration method for the analytical treatment of partial differential equations in fluid mechanics. The Caputo sense is used to describe fractional derivatives. The time-fractional Kaup-Kupershmidt (KK) equation is investigated, as it is the solution of the system of partial differential equations via the Boussinesq-Burger equation. By comparing the results that are obtained by the variational iteration method with those obtained by the two-dim

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <

In this study, an efficient compression system is introduced, it is based on using wavelet transform and two types of 3Dimension (3D) surface representations (i.e., Cubic Bezier Interpolation (CBI)) and 1 st order polynomial approximation. Each one is applied on different scales of the image; CBI is applied on the wide area of the image in order to prune the image components that show large scale variation, while the 1 st order polynomial is applied on the small area of residue component (i.e., after subtracting the cubic Bezier from the image) in order to prune the local smoothing components and getting better compression gain. Then, the produced cubic Bezier surface is subtracted from the image signal to get the residue component. Then, t

  This paper deals  the prediction of the process of  random spatial data of two properties, the first is called  Primary variables  and the second is called secondary  variables ,   the method  that were used in the  prediction process for this type  of data is technique Co-kriging  , the method is usually used when the number of primary variables  meant to predict for one of its elements is measured in a particular location a few (because of the cost or difficulty of obtaining them) compare with secondary variable which is the number of elements  are available and  highly correlated with primary variables, as was the&nbs

This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),

In this paper, a discrete- time ratio-dependent prey- predator model is proposed and analyzed. All possible fixed points have been obtained. The local stability conditions for these fixed points have been established. The global stability of the proposed system is investigated numerically. Bifurcation diagrams as a function of growth rate of the prey species are drawn. It is observed that the proposed system has rich dynamics including chaos.

DC planar sputtering system is characterized by varying discharge potential of (250-2000 volt) and Argon gas pressures of (3.5×10-2 – 1.5) mbar. The breakdown voltage for silver electrode was studied with a uniform electric field at different discharge distances, as well as plasma parameters. The breakdown voltage is a product of the Argon gas pressure inside the chamber and gab distance between the electrodes, represent as Paschen curve. The Current-voltage characteristics curves indicate that the electrical discharge plasma is working in the abnormal glow region. Plasma parameters were found from the current-voltage characteristics of a single probe positioned at the inter-cathode space. Typical values of the electron temperature an

The paper aims to identify the impact of discrete realization strategy in the development of reflective thinking among students: (males/females) of Qur'an and Islamic education departments for the course of Islamic jurisprudence according to the variability of sex. The researcher used the experimental approach and adopted an experimental determination with a set part of the two groups (experimental and controlled). He selected the sample deliberately which consists of (147) students spread over four classes (experimental males/ experimental females/ controlled males/ controlled females), and it took last for an academic year of (2010-2011). He, then, prepared a post test to measure the reflective thinking with his five skills (skill of o