Power system stabilisers (PSSs) are supplementary controllers connected to the excitation system of synchronous generators to damp electromechanical oscillations. Multi-band PSSs are reported as advanced PSSs with the ability to damp out all oscillation modes present in the power systems. This study presents the design of a robust fractional-order multi-band power system stabiliser (Fo-MBPSS) using a meta-heuristic hybrid algorithm for dynamic stability improvement of multi-machine power systems. The large bandwidth, memory effect and flat phase contribution in the frequency response of fractional-order controllers are exploited to make the Fo-MBPSS perform well against a wide range of system uncertainties. The parameter tuning problem of Fo-MBPSS is transformed to an optimisation problem that is solved using a hybrid algorithm by combining a dynamic genetic algorithm (DGA) with a standard particle swarm optimisation (PSO) algorithm. The performance of the proposed DGA-PSO-Fo-MBPSS is evaluated through eigenvalue analysis, non-linear time-domain simulations and some performance indices, in two different multi-machine systems under different loading conditions and disturbances. The results are compared with PSO-based conventional MBPSS and PSO based Fo-MBPSS (PSO-Fo-MBPSS) to establish the fractional parameter effect on the improvement of the system dynamic response and the relevance of the proposed hybrid optimisation technique in achieving robustness.