Dynamic analysis of the fractional distributed delay models

Abstract

Abstract In this paper, we analyze the stability of the fractional distributed delay models. We use the linear chain trick to convert these models into an incommensurate fractional order systems. We get the stability regions by studying the characteristic equation around equilibrium points. We investigate how the fractional order $$\alpha _{1}$$ , $$\rho$$ and a affect the stability of the models. We study the fractional order delay logistic equation and compare the influence of the distributed delay on the stability regions. Numerical simulations are exhibited to confirm the analytical results.