Fractional-based approach in neural networks for identification problem

This paper proposes a new approach to the neural networks. This approach is based on the fractional-order concept and suggests a new formulation for the neural network in parameter identification problem. From this, continues Hopfield net is chosen and extended to the fractional net in which fractional-order equations describe its dynamical structure. As Hopfield networks have no determined learning law, here, a design method based on network energy function, will be developed for parameter identification problem. To reach our goal, the objective function formed to be minimized, should be appeared in the form of Hopfield energy function and through that, weight and bias matrices will be determined. To have a comparison between standard Hopfield network and its fractional-based approach, an illustrative example of fractional-order system is considered. The simulation results promises some salient advantages of the fractional based approach for the neural network.