Generalized Fractional Calculus for Gompertz-Type Models

This paper focuses on the construction of deterministic and stochastic extensions Gompertz curve by means generalized fractional derivatives induced complete Bernstein functions. Precisely, we first introduce a class linear equations involving integral study properties its solutions. is done proving existence uniqueness Gaussian solutions such via fixed point argument then showing that, under suitable conditions, expected value solution solves equation. Regularity absolute p-moment functions proved using Grönwall inequalities. Deterministic curves are introduced Caputo-type derivatives, possibly with respect to other Their counterparts constructed previously considered define rate process generalization lognormal distributions ensure that median newly coincides curve.