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

Regression Discontinuity (RD) means a study that exposes a definite group to the effect of a treatment. The uniqueness of this design lies in classifying the study population into two groups based on a specific threshold limit or regression point, and this point is determined in advance according to the terms of the study and its requirements. Thus , thinking was focused on finding a solution to the issue of workers retirement and trying to propose a scenario to attract the idea of granting an end-of-service reward to fill the gap ( discontinuity point) if it had not been granted. The regression discontinuity method has been used to study and to estimate the effect of the end -service reward on the cutoff of insured workers as well as t

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.  

level of effectiveness of Glutathione - S - Transferees (GST), Glutathione peroxides (GPX),Malondialdehyde (MDA) the product of lipid peroxidation and some trace elements ( zinc,seleinum,iron ,copper ) had been measured in sera of (50) women with breast disease.which had been divided to : Control group (25),The first group (A) benign breast tumors (25),the second group (B) breast cancer (25). The results showed a clear moral high level of Glutathione - S - Transferees (GST), Glutathione peroxidase (GPX) , and Malondialdehyde (MDA) level in breast cancer group while a slight increase were observed in the levels of these enzymes and(MDA) in benign breast group. A significant reduction was evident in the levels of selenium and zinc

The aim of this study is to evaluate the levels of trace elements Magnesium (Mg), Zinc (Zn), Copper (Cu), and Selenium (Se) in blood sera of asthmatic patients by Atomic Absorption Spectrophotometry (AAS). The concentrations of Mg, Cu, and Zn have been determined by Flame Atomic Absorption spectrophotometry (FAAS), and Se with flameless Graphite Furnace Atomic Absorption Spectrophotometry (GFAAS). The study involves (55) asthmatic patients as study group and (28) subjects as control from both genders. Serum levels of Mg, Cu, and Se were significantly higher (p<0.001 for all) in patients when compared with healthy subjects, while Zn level was relatively significant (p<0.05). Our observations confirm the efficacy and applicability of (AAS) in