The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

This paper discusses the method for determining the permeability values of Tertiary Reservoir in Ajeel field (Jeribe, dhiban, Euphrates) units and this study is very important to determine the permeability values that it is needed to detect the economic value of oil in Tertiary Formation. This study based on core data from nine wells and log data from twelve wells. The wells are AJ-1, AJ-4, AJ-6, AJ-7, AJ-10, AJ-12, AJ-13, AJ-14, AJ-15, AJ-22, AJ-25, and AJ-54, but we have chosen three wells (AJ4, AJ6, and AJ10) to study in this paper. Three methods are used for this work and this study indicates that one of the best way of obtaining permeability is the Neural network method because the values of permeability obtained be

Abstract :In this study, amygdaline in Iraqi plant seeds was extracted and isolated from their seeds matrix using reflux procedure and subsequently identified and determined by high performance liquid chromatography (HPLC) on reversed phase column of LC-18 (150mm x 4.6mm, 5?m )with actonitrile :water ( 50 : 50 ) as mobile phase at flow rate of ( 0.5 mL/min ) and detection at wavelength of 215 nm.The experimental results indicated that the linearity of calibration is in the range of 1.0-30.0 mg L-1amygdaline with the correlation coefficient of 0.9949. The limit of detection (LOD) and limit of quantitation (LOQ) for amygdaline were of 0.88 and 2.93 mg L-1 in standard pure sample. The mean recovery percent is 97.34±0.58 at 95% confidence inte

This paper proposes a new structure for a Fractional Order Sliding Mode Controller (FOSMC) to control a Twin Rotor Aerodynamic System (TRAS). The new structure is composed by defining two 3-dimensional sliding mode surfaces for the TRAS model and introducing fractional order derivative integral in the state variables as well as in the control action. The parameters of the controller are determined so as to minimize the Integral of Time multiplied by Absolute Error (ITAE) performance index. Through comparison, this controller outperforms its integer counterpart in many specifications, such as reducing the delay time, rise time, percentage overshoot, settling time, time to reach the sliding surface, and amplitude of chattering in control inpu

The main purpose of this paper, is to characterize new admissible classes of linear operator in terms of seven-parameter Mittag-Leffler function, and discuss sufficient conditions in order to achieve certain third-order differential subordination and superordination results. In addition, some linked sandwich theorems involving these classes had been obtained.  

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

 هدف البحث التعرف الى اسباب سلوك التنمر لدى طلاب الصف الاول المتوسط من وجهة نظر المدرسين والمدرسات واساليب تعديله، واستعمل الباحثان المنهج الوصفي واختيار عينة عشوائية من المدرسين والمدرسات في متوسطة أرض الرافدين ومتوسطة الرحمن للبنين وكان عددهم (46) مدرساً ومدرسة بواقع (32) مدرساً و(14) مدرسة، واعتمد الباحثان الاستبانة أداة للتعرف الى اسباب سلوك التنمر واساليب تعديله، واشارت نتائج البحث الى تنوع اسباب التن