%A Turalska,Malgorzata
%A West,Bruce J.
%D 2018
%J Frontiers in Physics
%C
%F
%G English
%K fractional calculus,subordination,inverse power law,complex networks,Control
%Q
%R 10.3389/fphy.2018.00110
%W
%L
%N 110
%M
%P
%7
%8 2018-October-16
%9 Original Research
%#
%! Fractional Dynamics of Individuals in Complex Networks
%*
%<
%T Fractional Dynamics of Individuals in Complex Networks
%U https://www.frontiersin.org/article/10.3389/fphy.2018.00110
%V 6
%0 JOURNAL ARTICLE
%@ 2296-424X
%X The relation between the behavior of a single element and the global dynamics of its host network is an open problem in the science of complex networks. We demonstrate that for a dynamic network that belongs 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.