A numerical estimation of the fractional-order Liouvillian systems and its application to secure communications

This paper introduces a method for the numerical estimation of the fractional derivative of a signal, a smoothed sliding modes state observer is used to make the estimation. As application for the estimator a color image encryption algorithm is given, the algorithm is based on the synchronisation of fractional chaotic Liouvillian systems and its main characteristics are the capability to keep data safe from the most common types of cryptanalysis and handling large colour images while producing no data loss.