Cyber-Physical Systems as General Distributed Parameter Systems: Three Types of Fractional Order Models and Emerging Research Opportunities

TL;DR

This paper introduces three types of fractional order models for cyber-physical systems as distributed parameter systems, exploring their relationships and highlighting future research directions in modeling complex natural and physical phenomena.

Contribution

It presents a unified framework of three fractional operator-based models for CPSs, expanding the modeling tools for complex systems with fractional dynamics.

Findings

Exploration of relationships among fractional Laplacian, fractional power, and fractional derivative models.

Identification of potential applications in modeling anomalous diffusion phenomena.

Discussion of future research opportunities in fractional order modeling of CPSs.

Abstract

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.