Some applications of fractional order calculus

By Andrzej Dzielinski, Dominik Sierociuk, Grzegorz Sarwas. 2010

217 citations recorded by the source corpus.

Abstract. This paper presents some recent results in the area of application of fractional order system models. After the introduction to the dynamic systems modelling with the fractional order calculus the paper concentrates on the possibilities of using this approach to the modelling of real-world phenomena. Two examples of such systems are considered. First one is the ultracapacitor where fractional order models turn out to be more precise in the wider range of frequencies than other models used so far. Another example is the beam heating problem where again the fractional order model allows to obtain better modelling accuracy. The theroetical models were tested experimentally and the results of these experiments are described in the paper.

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/73433515c72bcf37993c37d4477164ada8ffbd24

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In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost (2020, methodology): “applications of the use of the fractional calculus are in the modeling of an ultracapacitor [2], viscoelastic materials [3], the heating process [4] and in time-fractional diffusion equations on a metric graph [44].”
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems (2017, background): “…mechanics (Mainardi, 1997), colored noise (Mandelbrot, 1967) and others (see Debnath, 2003; Bohannan, 2008; Das, 2008; Dalir and Bashour, 2010; Dzielinski et al., 2010; Hilfer, 2012; Jiang and Ding, 2013; Machado et al., 2013; Irandoust-Pakchin et al., 2014), fractional calculus has become…”