Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

In this paper, the possibilities of expressing natural response a linear commensurate fractional-order system (FOS) as combination basis functions are analyzed. For all possible types sα-domain poles, corresponding found, kernel which is two-parameter Mittag–Leffler function Eα,β, β = α. It pointed out that there mutually unambiguous correspondences between FOS and known integer-order (IOS) for α 1. This correspondence can be used to algorithmically find analytical formulas impulse responses when characteristics IOS known. shown generated with Podlubny‘s type εk (t, c; α, α), where c k pole its multiplicity, respectively.