Fractional-order dynamics in a random, approximately scale-free network of agents

Differential equations with fractional-order derivatives, e.g., the "one-half" derivative, have a long history in mathematics, but have not yet attained mainstream use in engineering and applied science. While applications do exist in modeling specific phenomena such as visco-elasticity and other types of difficult-to-model phenomena, and extensions to control such as in fractional-order PID do exist, everyday use of fractional order modeling is uncommon. A subset of complex systems called Cyber-Physical Systems (CPS) is receiving much emphasis in the research community. In this paper we show examples of networked system models which exhibit fractional-order dynamic responses. This suggests that fractional-order dynamics may be prevalent in CPS and hence may be an important and useful modeling tool in that area. We particularly focus on a scale free networked system.