Abstract:In this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of sα-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag–Leffler function Eα,β, β = α. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) … Show more
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