Separation of solutions and the attractivity of fractional-order positive linear delay systems with variable coefficients

This article has two purposes. First, we study the separation of solutions to mixed-order positive linear delay systems with variable coefficients and the lower estimates of the separation of solutions to those systems. Second, we consider the global attractivity of fractional-order positive linear delay systems and describe precisely the rate of convergence of solutions to their equilibrium in some specific cases. To do this, the unified approach we use here is that the comparison principles have been modified to accommodate fractional-order delay systems. In addition, numerical simulations are introduced to illustrate the validity of the theoretical results. •We prove the separation of solutions to multi-order fractional positive linear delay systems with variable coefficients.•We show the lower estimates of solutions to such systems.•Using comparative arguments, we search for different criteria to characterize the attraction of solutions to multi-order fractional positive linear systems with variable coefficients and bounded delays.•In addition, in the case when the fractional orders are equal, we describe precisely the rate of convergence of the solutions to the origin.•Numerical simulations are provided to illustrate the validity of the theoretical results.