We propose and experimentally demonstrate repetition-rate multiplication of picosecond optical pulse trains by a fractional factor based on temporal self-imaging, involving temporal phase modulation and first-order dispersion. Multiplication factors of 1.25, 1.33, 1.5, 1.6, 1.75, 2.25, 2.33 and 2.5 are achieved with high fidelity from a mode-locked laser with an input repetition-rate between 10 and 20 GHz.