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.

Double skin ventilated roof is one of the important passive cooling techniques that aims to reduce solar heat gain through roofs by reducing both the conduction and convection heat transfer from the roof to the ceiling of buildings. On the other hand, radiant barrier system (RBS) is very powerful in blocking the radiation heat transfer between the two skins. In this research,the effect of placing a thin layer of aluminium foil at different locations on the thermal insulation performance of a double skin ventilated roof model is investigated experimentally and the optimum location that transmits less heat flux from the lower skinis specified.The model is made of two parallel inclined galvanized steel plates. Galvanized steel has been used

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.

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.

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.

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

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

The present paper deal with the issue of the beginning of the culturally
renaissance in emirates of Arab Gulf from 1914-1945 between tow world war
has been attracting the attention of academic about the developments in many
fields in the Arab Gulf at this time.
The paper is divided into five sections. First section, deals with the
geographic importance for the Arab Gulf region. Second section, the economic
situations in the region before and after oil. The third section, talk for social
situations, like population, tribe and tribes in society, and immigration. The
fourth section, deals with the factors of rise the culture and political in the Arab
Gulf before discovery of oil period. The five section, the cultu