AUTHOR=Turalska Malgorzata , West Bruce J. 

TITLE=Fractional Dynamics of Individuals in Complex Networks

JOURNAL=Frontiers in Physics

VOLUME=Volume 6 - 2018

YEAR=2018

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00110

DOI=10.3389/fphy.2018.00110

ISSN=2296-424X

ABSTRACT=The dependence of the behavior of a single individual on the global dynamics of the social network to which it belongs is an open problem in sociology. We demonstrate that for a dynamical network belonging to the Ising universality class this problem can be approached analytically through a subordination procedure. The analysis leads to a linear fractional differential equation of motion for the average trajectory of the individual, whose analytic solution for the probability of changing states is a Mittag-Leffler function. Consequently, the analysis provides a linear description of the average dynamics of an individual, without linearization of the complex network dynamics.