We introduce a fractional single-file diffusion (FSFD) model describing the stochastic evolution of an assembly of nonpassing particles (single-file (SF) system), where in addition to the excluded-volume interaction between the particles, they individually follow sticky trajectories (fractional diffusion (FD)) on a fractal support. While the long-range correlations between the particles mediated through the former interaction is treated through the reflection principle, the sticky trajectories involve fractional time derivatives whose order is distributed over the interval from zero to one. A detailed study of the propagators of FSFD is made and compared with the normal SF diffusion through their time evolution in state space. Both the diffusion mechanisms, SF and FD, are known for anomalous subdiffusive behaviour; their combined entity, FSFD has been found to exhibit further anomality leading to ultraslow diffusion. Through an integral transformation of the Gaussian propagator, a generalised expression for the mean square displacement of a tagged particle undergoing FSFD is obtained.