  Production cross sections of muons from semi-leptonic decays of charm and
beauty hadrons were measured at forward rapidity ($2.5<y<4$) in proton--proton
(pp) collisions at a centre-of-mass energy $\sqrt{s}=5.02$ TeV with the ALICE
detector at the CERN LHC. The results were obtained in an extended transverse
momentum interval, $2 < p_{\rm T} < 20$ GeV/$c$, and with an improved precision
compared to previous measurements performed in the same rapidity interval at
centre-of-mass energies $\sqrt{s}= 2.76$ and 7 TeV. The $p_{\rm T}$- and
$y$-differential production cross sections as well as the $p_{\rm
T}$-differential production cross section ratios between different
centre-of-mass energies and different rapidity intervals are described, within
experimental and theoretical uncertainties, by predictions based on
perturbative QCD.
