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Laguerre-type special functions and population dynamics. (English) Zbl 1117.33001
Recently, 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): $$D_{nL}:=Dx\ldots DxDxD.$$ 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.

MSC:
33B10Exponential and trigonometric functions
33C45Orthogonal polynomials and functions of hypergeometric type
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References:
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