Global stability of a fractional order eco-epidemiological system with infected prey

A fractional order eco-epidemiological system with infected prey is proposed and studied. Threshold parameters are obtained to determine the existence and stability conditions of equilibrium points of the proposed fractional order system. In order to clarify the characteristics of the proposed fractional order system, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions, as well as the stability conditions of the system are examined. The global properties of all biologically feasible equilibrium points are studied by constructing suitable Lyapunov functions. It is proved that all equilibrium points of the proposed fractional order system are globally stable whenever they are locally stable. Some numerical simulations are conducted to verify the theoretical results.