Brilhante, M. FátimaGomes, M. IvetteMendonça, SandraPestana, DinisPestana, Pedro2023-03-282023-03-282023-02-152504-3110http://hdl.handle.net/10400.14/40736Logistic and Gompertz growth equations are the usual choice to model sustainable growth and immoderate growth causing depletion of resources, respectively. Observing that the logistic distribution is geo-max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, we investigate other models proportional to either geo-max-stable distributions (log-logistic and backward log-logistic) or to other max-stable distributions (Fréchet or max-Weibull). We show that the former arise when in the hyper-logistic Blumberg equation, connected to the Beta (Formula presented.) function, we use fractional exponents (Formula presented.) and (Formula presented.), and the latter when in the hyper-Gompertz-Turner equation, the exponents of the logarithmic factor are real and eventually fractional. The use of a BetaBoop function establishes interesting connections to Probability Theory, Riemann–Liouville’s fractional integrals, higher-order monotonicity and convexity and generalized unimodality, and the logistic map paradigm inspires the investigation of the dynamics of the hyper-logistic and hyper-Gompertz maps.engBeta and BetaBoopExtreme and geo-extreme distributionsFractional calculusGeneralized convexity and unimodalityHyper-logistic and hyper-Gompertz growthNonlinear mapsjournal article10.3390/fractalfract702019485148911001