Several non-linear behaviors in scales space, in the framework of Scale Relativity Theory, are highlighted. All these are possible through the employment of fractal-type Airy functions, which allow a revaluation of the wave/corpuscle duality, from the perspective of a fractal paradigm. In such a context, it is possible to distinguish the prevalence of either the corpuscle character, or of the wave character, in any experiment which implies microparticles.