  This work analyzes fractional continuous-time random walks on two-layer
multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson
distribution of a walker to become active, while a jump to one of its neighbors
depends on the connection weight. Synthetic multiplexes with well known
topology are used to illustrate dynamical features obtained by numerical
simulations, while exact analytical expressions are presented for multiplexes
assembled by circulant layers with finite number of nodes. Special attention is
given to the effect of inter- $D_x$ and intra-layer $D_i$ coefficients on the
system's behavior. In opposition to usual discrete time dynamics, the
relaxation time has a well defined minimum at an optimal value of $D_x/D_i$. It
is found that, even for the enhanced diffusion condition, the walkers mean
square displacement increases linearly with time.
