  Cyber-physical systems (CPSs) are man-made complex systems coupled with
natural processes that, as a whole, should be described by distributed
parameter systems (DPSs) in general forms. This paper presents three such
general models for generalized DPSs that can be used to characterize complex
CPSs. These three different types of fractional operators based DPS models are:
fractional Laplacian operator, fractional power of operator or fractional
derivative. This research investigation is motivated by many fractional order
models describing natural, physical, and anomalous phenomena, such as
sub-diffusion process or super-diffusion process. The relationships among these
three different operators are explored and explained. Several potential future
research opportunities are then articulated followed by some conclusions and
remarks.
