Dynamics of annealed systems under external fields: CTRW and the fractional Fokker-Planck equations

We consider the linear response of a system modelled by continuous-time random walks (CTRW) to an external field pulse of rectangular shape. We calculate the corresponding response function explicitly and show that it exhibits aging, i.e. that it is not translationally invariant in the time domain. This result differs from that of systems which behave according to fractional Fokker-Planck equations.