The principles presented in this paper for the case of mechanical impedance are in essence equivalent to what has been termed the generalized Vincent circle by other authors.
The other one is termed the generalized Riccati transformation technique; we refer the reader to Li [11], Li et al. [12], Li and Saker [13], and the related references cited therein.
The models generalize the two-mutation model of Moolgavkar, Venzon, and Knudson, and also the Armitage-Doll model, and will be termed the generalized MVK model.
Although the new generalization of the HP distribution has an extra parameter, it is computationally not more complicated than the HP since it retains the two-term probability recurrence formula and the normalizing constant, in terms of the generalized Mittag-Leffler function, is readily computed.
The controlled system is studied in terms of the generalized plant description, as it is common in robust control design.
This was done by Lui et al. (2007) who evaluated all the terms in the generalized Ohm's law during current disruption activity unconnected with magnetic reconnection.
In [3], the author considered the function φ u, b, c ( z ) defined, in terms of the generalized Bessel function ω u, b, c ( z ).
Next we give an interesting series representation for ζ ( 2 r ) in terms of the generalized zeta functions ζ ( 2 r + 1, j + 1 ) ( j ∈ N 0 ).
We also obtained the fractional generalization of the one-sided and two-sided Green's function in terms of the generalized Mittag-Leffler function.
The solutions, obtained by means of Laplace and Hankel transforms, are presented in integral and series forms in terms of the generalized G-function.
