In this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. We analyze the existence and stability of all possible equilibria. Numerical simulations reveal that anti-predator behaviour not only makes the coexistence of the prey and predator ...

in this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. we analyze the existence and stability of all possibleequilibria. numerical simulations reveal that anti-predator behaviour notonly makes the coexistence of the prey and predator po...

This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

In this paper, we have introduced a fractional-ordered predator-prey population model which has been successfully solved with the help of two powerful analytical methods, namely, Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The fractional derivatives are described in the Caputo sense. Using initial values, we have derived the explicit solutions of predator-prey pop...

Abstract In this research, we discuss the influence of an infectious disease in evolution ecological species. A computational predator-prey model fractional order is considered. Also, assume that there a non-fatal developed prey population. Indeed, it considered predators have cooperative hunting. This situation occurs when pair or group animals coordinate their activities as part hunting behav...

A prey–predator system with logistic growth of prey and hunting cooperation predators is studied. The introduction fractional time derivatives the related persistent memory strongly characterize model behavior, as many dynamical systems in applied sciences are well described by such fractional-order models. Mathematical analysis numerical simulations performed to highlight characteristics propo...