Considering harmonic evolution of the magnetic induction field, we establish a link between a time domain, high amplitude, fractional hysteresis model and the frequency domain, weak amplitude, fractional, ferromagnetic Cole-Cole model. A relation between α (the fractional order), τ (the relaxing time) and ρ (the dynamic constant) can be set. Experimental results performed on a typical soft ferromagnetic (Fe-Si) validate the theory. Correct comparison simulations/measures are observed for both situations (weak and high amplitude excitation) conserving the same set of parameters (α, τ, ρ). The dynamic behavior of a ferromagnetic sample can be set under weak amplitude excitation using simple impedance LCR meter characterization and conserved for the simulation of high amplitude dynamic hysteresis cycles.