In the framework of Fractal Theory of Motion for the Scale Relativity Theory with arbitrary and constant fractal dimensions, dynamics in complex systems associated to the fractal-non-fractal transition are analyzed. Working with the assumption that these dynamics are described by means of fractal curves, Lorenz type behaviors become "operational" through a Galerkin method. Then Rayleigh and Prandtl effective numbers are specified both by means of classical kinetic coefficients and scale resolution while the dynamics variables act as the limit of a family of mathematical functions, non-differentiable for non-null scale resolution.