2015/09/07 by Fudong Ge, Ge, Fudong, YangQuan Chen +3
Mathematics · #35J05 #35R11 #68M14 #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods for differential equations #math.CA #msc:35J05 #msc:35R11 #msc:68M14
paper · pdf · doi:10.48550/arxiv.1509.04318
12 pages, 0 figures, IEEE/CAA Journal of Automatica Sinica, 2015
arxiv created 2015/09/07 · openalex publication_date 2015/09/07 · arxiv updated 2015/09/16 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01
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.