Tritrophic fractional model with Holling III functional response

In this paper, we analyzed the local stability of three species in two fractional tritrophic systems, with Caputo's fractional derivative and Holling type Ⅱ and Ⅲ functional responses, when the prey density has a linear growth. To begin, we obtained the equilibria in the first octant under certain conditions for the parameters. Subsequently, through linearization and applying the Routh-Hurwitz Criterion, we concluded that only the system with Holling type Ⅲ exhibits an asymptotically stable equilibrium point, where the fractional derivative order belongs to the interval $(0,1]$. Finally, we obtained the solution of the system with the Holling type Ⅲ functional response, using the multistage homotopic perturbation method, and presented an example that shows the dynamics of the solutions around the stable equilibrium point.