On disappearance of chaos in fractional systems

In the present article we take a survey of present literature on chaotic behavior of fractional order dynamical systems. Further we numerically explore fractional Chen, Rössler, Bhalekar-Gejji, Lorenz and Liu systems and observe that chaos always disappear if Σ ≤ 2. The existing examples in the literature along with the systems that we have analyzed lead us to conjecture non-existence of chaos if Σ ≤ 2; which in some sense is a generalization of classical Poincaré-Bendixon theorem for FODS.