Measurements of the branching fractions for the semileptonic decays ${D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}$, $\varphi {\mu }^{+}{\nu }_{\mu }$, $\eta {\mu }^{+}{\nu }_{\mu }$ and ${\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$

By analyzing $482\text{}\text{}{\mathrm{pb}}^{-1}$ of ${e}^{+}{e}^{-}$ collision data collected at the center-of-mass energy $\sqrt{s}=4.009\text{}\text{}\mathrm{GeV}$ with the BESIII detector, we measure the branching fractions for the semi-leptonic decays ${D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}$, $\varphi {\mu }^{+}{\nu }_{\mu }$, $\eta {\mu }^{+}{\nu }_{\mu }$ and ${\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$ to be $B\left({D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}\right)=\left(2.26±0.45±0.09\right)%$, $B\left({D}_{s}^{+}\to \varphi {\mu }^{+}{\nu }_{\mu }\right)=\phantom{\rule{0ex}{0ex}}\left(1.94±0.53±0.09\right)%$, $B\left({D}_{s}^{+}\to \eta {\mu }^{+}{\nu }_{\mu }\right)=\left(2.42±0.46±0.11\right)%$ and $B\left({D}_{s}^{+}\to {\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }\right)=\left(1.06±\phantom{\rule{0ex}{0ex}}0.54±0.07\right)%$, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions for the three semi-muonic decays ${D}_{s}^{+}\to \varphi {\mu }^{+}{\nu }_{\mu },\eta {\mu }^{+}{\nu }_{\mu }$ and ${\eta }^{\prime }{\mu }^{+}{\nu }_{\mu }$ are determined for the first time and that of ${D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}$ is consistent with the world average value within uncertainties.