In this paper, the initialization of fractional order systems is analyzed. The objective is to prove that the usual pseudostate variable is unable to predict the future behavior of the system, whereas the infinite dimensional variable fulfills the requirements of a true state variable. Two fractional systems, a fractional integrator and a one-derivative fractional system, are analyzed with the help of elementary tests and numerical simulations. It is proved that the dynamic behaviors of these two fractional systems differ completely from that of their integer order counterparts. More specifically, initialization of these systems requires knowledge of initial condition.
Initial Conditions and Initialization of Fractional Systems
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 15, 2015; final manuscript received January 28, 2016; published online March 16, 2016. Assoc. Editor: Gabor Stepan.
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Tari, M., Maamri, N., and Trigeassou, J. (March 16, 2016). "Initial Conditions and Initialization of Fractional Systems." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041014. https://doi.org/10.1115/1.4032695
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