Fractional differential equations with bio-medical applications

Abstract

In this chapter, we investigate the dynamics of fractional order models in bio-medical. First, we examine the fractional order model of HIV Infection and analyze the stability results for non-infected and infected equilibrium points. Then, we concentrate on the fractional order tumor growth model and establish a sufficient condition for existence and uniqueness of the solution of the fractional order tumor growth model. Local stability of the four equilibrium points of the model, namely the tumor free equilibrium, the dead equilibrium of type 1, the dead equilibrium of type 2 and the coexisting equilibrium is investigated by applying Matignons condition. Dynamics of the fractional order tumor model is numerically investigated by varying the fractional-order parameter and the system parameters. © 2019 Walter de Gruyter GmbH, Berlin/Boston.