In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.

Humanity has Suffered Greatly from the Economic crisis and instability, Before the Emergence of the rule of the Capitalist System, However, the reaons were Different. But almost Completely Contradictory. At a time When the Causes of the Crisis was due to the time Factor is the product of failure of productie forces, Bears modern Crises resoled by the progress that is in the embrace of the abundance, and as far as lies in the nature and content of the capitalist system itselfas a system based on the creation of productive capacities in excess unable to accomplish through demand by the chaos of production based,  on the logic of the market on one hand, and the nature of the output and direction. On the other hand the relations

     In this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip ti

in this paper fourth order kutta method has been used to find the numerical solution for different types of first liner

In this paper, the author established some new integral conditions for the oscillation of all solutions of nonlinear first order neutral delay differential equations. Examples are inserted to illustrate the results.

This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.

      In this paper fractional Maxwell fluid equation has been solved. The solution is in the Mettag-Leffler form. For  the corresponding solutions for ordinary Maxwell fluid are obtained as limiting case of general solutions. Finally, the effects of different parameters on the velocity and shear stress profile are analyzed through plotting the velocity and shear stress profile.

The current article focuses on studying the social organization reality of the Iraqi society; it aims to construct an Iraqi organized personality that believe in the principles of Islamic religion by making use of the sociology thoughts in explaining the strength of social organization, and the causes of social deviance in attempt of decreasing the deviance and strengthening the cohesion of Iraqi character.

The researchers put forward some questions: to what extent the western theoretical pattern can succeed in explaining the social organization of the Iraqi society? What is the more appropriate western theory for diagnosing the cohesion and deviance of the society? What is the s

In this paper an atmometer apparatus were used in the greenhouses for estimating reference evapotranspiration values. Experimental work was conducted in the agriculture research center in the College of Agriculture-University of Baghdad west of the city of Baghdad. One atmometer was used in eggplant greenhouse and in cucumber greenhouse through the winter growing season 2013-2014. FAO Penman-Monteith equation was applied outside the greenhouse and used only 65% from the value of ET_o in the greenhouses for estimating the reference evapotranspiration in the greenhouse. Moreover, Penman-Monteith equation was applied in greenhouses for the evaluating the performance of the atmometer. The results show that the erro