Laguerre-type special functions and population dynamics.

*(English)*Zbl 1117.33001Recently, in a series of papers, P. E. Ricci and his collaborators investigated some Laguerre-type special functions obtained by the use of the Laguerre derivative operators (containing $n+1$ derivatives):

$${D}_{nL}:=Dx...DxDxD\xb7$$

In this paper, the authors introduce new Laguerre type population dynamics models by substituting in classical models the ordinary derivatives with the Laguerre derivatives. The eigenfunctions of ${D}_{nL}$ are useful in order to approximate different behavior of population growth. The corresponding Laguerre-type of modified logistic, Bernoulli, Gompertz, Allee and Beverton-Holt models were considered. It was shown for these cases that the oscillating asymptotic behavior of solutions takes the place of the ordinary monotonic one.

Reviewer: Youssef Ben Cheikh (Monastir)