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This paper addresses the qualitative theory of mixed-order positive linearcoupled systems with bounded or unbounded delays. First, we introduce a generalresult on the existence and uniqueness of solutions to mixed-order linearcoupled systems with time-varying delays. Next, we obtain the necessary andsufficient criteria which characterize the positivity of a mixed-order delaylinear coupled system. Our main contribution is in Section 5. More precisely,by using a smoothness property of solutions to fractional differentialequations and developing a new appropriated comparison principle for solutionsto mixed-order delayed positive systems, we prove the attractivity ofmixed-order non-homogeneous linear positive coupled systems with bounded orunbounded delays. We also establish a necessary and sufficient condition tocharacterize the stability of homogeneous systems. As a consequence of theseresults, we show the smallest asymptotic bound of solutions to mixed-orderdelay non-homogeneous linear positive coupled systems where disturbances arecontinuous and bounded. Finally, we provide numerical simulations to illustratethe proposed theoretical results.

Qualitative analysis of solutions to mixed-order positive linear coupled systems with bounded or unbounded delays