Fractional Calculus for Scientists and Engineers by Manuel Duarte Ortigueira

Author:Manuel Duarte Ortigueira
Language: eng
Format: epub, pdf
Publisher: Springer Netherlands, Dordrecht

(4.4)

provided that Re(s) > 0 or Re(s) < 0. So (4.4) represents two different systems depending on the adopted region of convergence. In the following we will assume to deal with causal systems, Re(s) > 0.

If we let and use the results obtained in Sect.​ 2.​7.​4 we obtain the Frequency Response, H(j?),

(4.5)

We must be careful about the definition of the fractional power of j? (see Sect.​ 2.​7.​4). With (4.5) we can get the Bode diagrams as in the usual systems. It is interesting to remark that the asymptotic amplitude Bode diagrams are constituted by straight lines with slopes that, at least in principle, may assume any value, contrarily to the usual case where the slopes are multiples of 20 dB/decade.

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