Opinion dynamics and fractional operators

The aim of the paper is to consider - in base on classical models and numerical simulations - fractional model of the type of Hegselmann and Krause (FHK) taking into account memory of states. One of our hypothesis is that fractional operators will include memory of the system to the whole process. Then we are going to examine and to do an analyze with verification of properties of this fractional model with discrete time. We are aware of the fact that a direct change of an operator can cause the uselessness of a system, thus we expect a necessity of changing of the definition of consensus and modification of parameters describing the systems.