In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator.  e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated.  e su‰cient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to con‹rm the theoretical results.

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect

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 interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values

This paper sheds the light on the vital role that fractional ordinary differential equations(FrODEs) play in the mathematical modeling and in real life, particularly in the physical conditions. Furthermore, if the problem is handled directly by using numerical method, it is a far more powerful and efficient numerical method in terms of computational time, number of function evaluations, and precision. In this paper, we concentrate on the derivation of the direct numerical methods for solving fifth-order FrODEs  in one, two, and three stages. Additionally, it is important to note that the RKM-numerical methods with two- and three-stages for solving fifth-order ODEs are convenient, for solving class's fifth-order FrODEs. Numerical exa

In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.