Laguerre-type special functions and population dynamics

Abstract We introduce new Laguerre-type population dynamics models. These models arise quite naturally by substituting in classical models the ordinary derivatives with the Laguerre derivatives and therefore by using the so called Laguerre-type exponentials instead of the ordinary exponential. The L-exponentials e n ( t ) are increasing convex functions for t  ⩾ 0, but increasing slower with respect to exp  t . For this reason these functions are useful in order to approximate different behaviors of population growth. We consider mainly the Laguerre-type derivative D t t D t , connected with the L-exponential e 1 ( t ), and investigate the corresponding modified logistic, Bernoulli and Gompertz models. Invariance of the Volterra–Lotka model is mentioned.