  Models with mixed origins of anomalous subdiffusion have been considered
important for understanding transport in biological systems. Here, one such
mixed model, the quenched trap model (QTM) on fractal lattices, is
investigated. It is shown that both ensemble- and time-averaged mean square
displacements (MSDs) show subdiffusion with different scaling exponents, i.e.,
this system shows weak ergodicity breaking. Moreover, time-averaged MSD
exhibits aging and converges to a random variable following the modified
Mittag--Leffler distribution. It is also shown that the QTM on a fractal
lattice can not be reduced to the continuous-time random walks, if the spectral
dimension of the fractal lattice is less than 2.
