Laguerre-type fractional parametric population dynamics models
Applicable Nonlinear Analysis, Volume 2, Issue 3, December 2025, Pages: 146–158
DIEGO CARATELLI
The Antenna Company, High Tech Campus 29, 5656 AE - Eindhoven, The Netherlands
Eindhoven University of Technology, PO Box 513, 5600 MB - Eindhoven, The Netherlands
PAOLO EMILIO RICCI
Mathematics Section, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 - Roma, Italia
Abstract
In a previous article, we used a parametric Laguerre-type operator, which behaves like an exponential with respect to its eigenfunction, to introduce parametric models of population dynamics. In this work, starting from the results obtained there, we compare them with those in which the ordinary derivative is replaced by the fractional one, represented by means of the classical Euler definition. The major difficulty of this extension consists in the fact that the eigenfunctions of the fractional case are not obtained simply by replacing the factorials with the corresponding values expressed through the Gamma function, but required a more in-depth analysis. This fact resulted in a greater analytical complexity of the coefficients through which the coefficients of the different fractional models considered are obtained, by recurrence. Some examples are shown, obtained by the first author, using the computer algebra system Mathematicac.
Cite this Article as
Diego Caratelli and Paolo Emilio Ricci, Laguerre-type fractional parametric population dynamics models, Applicable Nonlinear Analysis, 2(3), 146–158, 2025