Stability of fractional-order population growth model based on distributed-order approach

The stability of fractional-order nonlinear system is still an open problem. In this paper, the stability issue of the positive nonlinear fractional-order population growth model is investigated by using the distributed-order approach and the Lyapunov method. The unconditionally stability is derived, and it is shown that the fact of stability for the equilibrium of fractional-order population growth model is equivalent to the corresponding integer-order one. The order-dependent and order-independent cases are discussed, and some salient features of fractional-order and distributed-order systems are discussed as well. Two numerical examples are illustrated to validate the concepts, and to reveal the heredity of fractional-order systems.