In this paper, it has been studied that how the inner dimension of a fractional order system influences the maximum number of frequencies which may exist in oscillations produced by this system. Both commensurate and incommensurate systems have been considered to clarify the relationship between the inner dimension and maximum number of frequencies. It has been shown that although in commensurate fractional order systems, like integer order systems, the maximum number of frequencies is half of the inner dimension, in incommensurate systems the problem is significantly more complicated and the relationship between the inner dimension and maximum frequencies can not precisely determined. However, in this article, some upper and lower bounds, depending on the inner dimension, have been provided for the maximum frequencies of incommensurate systems.
Stability Boundary Order System Fractional Order System Undamped Oscillation Integer Order System
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Ahmad W, El-Khazali R, El-Wakil A (2001) Fractional-order Wien-bridge oscillator. Electr Lett 37:1110–1112CrossRefGoogle Scholar
Barbosa RS, Machado JAT, Vingare BM, Calderon AJ (2007) Analysis of the Van der Pol oscillator containing derivatives of fractional order. J Vib Control 13(9–10):1291–1301zbMATHCrossRefGoogle Scholar
Matignon D (1996) Stability result on fractional differential equations with applications to control processing. In: IMACS-SMC Proceedings. Lille, France, pp 963–968Google Scholar
Daftardar-Gejji V, Jafari H (2007) Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives. J Math Anal Appl 328:1026–1033zbMATHCrossRefMathSciNetGoogle Scholar
Deng W, Li C, L J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynam 48:409–416Google Scholar
Adams RA (2006) Calculus: a complete course, 6th edn. Addison Wesley, TorontoGoogle Scholar