Effect of fear in a fractional order prey–predator model with time delayed carrying capacity

Abstract

The Caputo technique is used in this article to analyze the fractional-order predator–prey scenario. Incorporating a delayed carrying capacity for the prey population and posing the impact of individual prey fear on predators are two aspects of this. We first provide the model’s formulation in terms of an integer order derivative, and subsequently we expand it to a fractional order system in terms of the Caputo derivative. The article contains a number of conclusions about the prerequisites for the model’s existence and uniqueness as well as the restrictions on the boundedness and positivity of the solution. To satisfy the requirements for the existence and uniqueness of the precise solution, the Lipschitz condition is applied. Within the local context, we have examined the stability of equilibrium points. Additionally, we investigated whether Hopf bifurcation may occur at the interior equilibrium point of our suggested model. We have used the Generalised Euler technique to approximatively solve the model. The suggested scheme’s dependability is indicated by the fact that the results produced using the current numerical approach converge to equilibrium for the fractional order. For our research, MATLAB was used to enable graphical representations and numerical simulations.