Implicit and fractional-derivative operators in infinite networks of integer-order components

Mihir Sen, John P. Hollkamp, Fabio Semperlotti and Bill Goodwine

Chaos, Solitons & Fractals, 2018, vol. 114, issue C, 186-192

Abstract: Complex engineering systems may be considered to be composed of a large number of simple components connected to each other in the form of a network. It is shown that, for some network configurations, the equivalent dynamic behavior of the system is governed by an implicit integro-differential operator even though the individual components themselves satisfy equations of integer order. The networks considered here are large trees and ladders with potential-driven flows and integer-order components in the branches. It has been known that in special cases the equivalent operator for the overall system in the time domain is a fractional-order derivative. In general, however, the operator is implicit without a known time-domain representation such as a fractional derivative would have, and can only be defined as a solution to an operator equation. These implicit operators, which are a generalization of commonly known fractional-order derivatives, should play an important role in the analysis and modeling of complex systems. This paper illustrates the manner in which they naturally arise in the modeling of integer-order networked systems.

Keywords: Implicit operators; Fractional derivatives; Integrodifferential operators (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:114:y:2018:i:c:p:186-192

DOI: 10.1016/j.chaos.2018.07.003

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