In this paper, we investigate with a time fractional-order derivative in a
three-species predator-prey model with the presence of prey social behavior. A
new approximation for predator-prey interaction in the presence of prey social
behavior has been considered. For the model analysis, the study has been divided
into two principal parts. First of all, we study the local stability of the equilibria and the existence of Hopf bifurcation. Then, for the numerical analysis, the
Caputo fractional derivative operator is utilized to approximate the numerical
solution of the model. An excellent agreement is seen between the numerical
results and the theoretical predictions.