Measurements of the branching fractions for the semi-leptonic decays $D^+_s\to\phi e^{+}\nu_{e}$, $\phi \mu^{+}\nu_{\mu}$, $\eta \mu^{+}\nu_{\mu}$ and $\eta'\mu^{+}\nu_{\mu}$

By analyzing 482 pb(-1) of e(+) e(-) collision data collected at the center-of-mass energy root s = 4.009 GeV with the BESIII detector, we measure the branching fractions for the semi-leptonic decays D-s(+) -> phi e(+)v(e), phi mu(+)v(mu), eta mu(+)v(mu) and eta'mu(+)v(mu) to be B(D-s(+) -> phi e(+)v(e)) = (2.26 +/- 0.45 +/- 0.09)%, B(D-s(+) -> phi mu+v(mu)) = (1.94 +/- 0.53 +/- 0.09)%, B(D-s(+) -> eta mu(+)v(mu)) = (2.42 +/- 0.46 +/- 011)% and B(D-s(+) -> eta'mu(+)v(mu)) = (1.06 +/- 0.54 +/- 0.07)%, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions for the three semi-muonic decays D-s(+) -> phi mu(+)v(mu), eta mu(+)v(mu) and eta'mu(+)v(mu) are determined for the first time and that of D-s(+) -> phi e(+)v(e) is consistent with the world average value within uncertainties.