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

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

God created man with a social nature, that is, man cannot live alone, but there must be a society associated with him. And when God addressed Adam, the first of His creation, he addressed him with the speech of the Muthanna to him and his wife. “This tree, then you will be among the wrongdoers” (Al-Baqara: 35), and thus was the divine discourse for the first human experience on earth. It accommodates a social relationship, which is (the family), husband and wife. And since a person needs to meet, as Ibn Khaldun said: (The human meeting is necessary, and the wise men express this by saying (the human being is of course civil)) (). And as it is known that with the meeting, relations arise from love and hate, cooperation and struggle, a

The research aimed at identifying the reality of electronic marketing in elite athletes. The researchers used the descriptive method on (193) athletes from different sports; individual and team. Direct questions and an electronic marketing scale were applied to conclude that athletic shows come first in most bought goods. The results showed that there is a difference between direct and electron shopping in favor of direct shopping. In addition to that, the results showed that sports federations do not provide athletes with proper apparels and equipment thus placing financial burdens on the athlete. Finally, the researchers concluded that language was not a barrier in electronic shopping, lack of safety and trust was the main barrier

هدفت الدراسة لالقاء الضوء على وضع المرأة في التعليم العالي في العراق خلال الاعوام الدراسية: 2008 - 2009, 2010 – 2011 و2011- 2012. تتيح القوانين والتعليمات في التعليم العالي في العراق فرص متكافئة للاناث والذكور للتسجيل في الدراسات الاولية والعليا، وكذلك عدم التمييز في الرواتب الشهرية للمنتسبين وفقا لنوع الجنس (الجندر ). بلغ متوسط عدد الاناث في مرحلة الدراسة الاولية في مؤسسات التعليم العالي في العراق لثلا

I came back and made my jewelery from the first research or studies known to man, and the oldest era and confirmed the problem of searching for the links of sweets and admiration of the magnificence of the effectiveness of the search for the importance of preserving the heritage of the Iraqi civilization in its original creative aspects. Metal in Iraq, Head Costume, Neck Costume, Party Costume (Hands and Legs). The main results of the research were;

1-Contemporary folk jewelry in Iraq was characterized by design units for use.

Dependence in the feed industry in the form of laboratory mold.