CNN with non-integer order cells

A new kind of cellular neural network (CNN) is introduced. Its feature consists of a state representation using q-order derivatives, with q being a non-integer quantity. This approach can be considered as a generalisation of the traditional CNN model, which is obtained from the one presented in the paper as a particular case setting q=1. It is shown that this more general CNN structure exhibits suitable performance in terms of processing speed. Various examples are reported to show the suitability of non-integer order CNNs.