caa a22 4500 445361255 CHVBK 20180317142915.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s11071-010-9895-z doi (NATIONALLICENCE)springer-10.1007/s11071-010-9895-z On the fundamental linear fractional order differential equation [Elektronische Daten] [Abdelfatah Charef, Hassene Nezzari] This paper deals with the rational function approximation of the irrational transfer function $G(s) = \frac{X(s)}{E(s)} = \frac{1}{[(\tau _{0}s)^{2m} + 2\zeta (\tau _{0}s)^{m} + 1]}$ of the fundamental linear fractional order differential equation $(\tau_{0})^{2m}\frac{d^{2m}x(t)}{dt^{2m}} + 2\zeta(\tau_{0})^{m}\frac{d^{m}x(t)}{dt^{m}} + x(t) = e(t)$, for 0<m<1 and 0<ζ<1. An approximation method by a rational function, in a given frequency band, is presented and the impulse and the step responses of this fractional order system are derived. Illustrative examples are also presented to show the exactitude and the usefulness of the approximation method. Springer Science+Business Media B.V., 2010 Fractional order differential equations nationallicence Irrational transfer function nationallicence Rational function nationallicence Charef Abdelfatah Département d'Electronique, Université Mentouri-Constantine, Route Ain El-bey, 25000, Constantine, Algeria aut Nezzari Hassene Département d'Electronique, Université Mentouri-Constantine, Route Ain El-bey, 25000, Constantine, Algeria aut Nonlinear Dynamics Springer Netherlands 65/3(2011-08-01), 335-348 0924-090X 65:3<335 2011 65 11071 https://doi.org/10.1007/s11071-010-9895-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9895-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Charef Abdelfatah Département d'Electronique, Université Mentouri-Constantine, Route Ain El-bey, 25000, Constantine, Algeria aut NATIONALLICENCE 700 1- Nezzari Hassene Département d'Electronique, Université Mentouri-Constantine, Route Ain El-bey, 25000, Constantine, Algeria aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/3(2011-08-01), 335-348 0924-090X 65:3<335 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer