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Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fish chaotic system. First, we derived the existence of a chaotic attractor in the fractional-order system and also synchronisation problem between two identical fractional-order chaotic systems is studied. Also, control design for the synchronisation with a suitable linear controller is tested in the response system. Finally, numerical simulation results are provided to confirm the theoretical analysis.