Abstract
Neuronal networks are used in different fields of science and technology due to their capacity to approximate nonlinear functions through the synaptic weights optimization. This work shows a new form of optimization for neuronal networks based in fractional calculus. The fractional adaptation algorithm proposed was used to identify mechanical, electrical and biological systems. In each of the experiments a comparison between the proposed fractal-fractional model and the conventional model (with derivation order equal to one) was made.