In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.

A taxonomic keys was established of book and bark lice Order Psocoptera to isolated insects in Iraq from different localities of Baghdad and Babylon provinces. Thirteen species belong to eight genera and five families have been studied and described in details, these species were recorded for the first time in Iraq. These species are: Belaphopsocus badonneli New, 1971; Belaphotroctes oculeris Bodonnel, 1973; Embodopsocosis newi Bodonnel, 1973; Epipsocus stigamaticus Mockeord, 1991; Lepinotus huoni Schmidt and New, 2008; Liposcelies decolor Peramane 1925 Liposcelies paeta Pearman 1942 Liposclies bostrychphila Badonnel 1931; Liposclies brunnea Mostchulsky 1852; Liposclies entoophila Enderlein 1907; Neopsocopsis minuscule Li 2002 ;

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

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 thir

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

in this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained

The aim of this paper is to present method for solving ordinary differential equations of eighth order with two point boundary conditions. We propose two-point osculatory interpolation to construct polynomial solution.