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The branching ratios of the semileptonic decay widths of the charm mesons areanalyzed, using three different models for the Isgur-Wise functions, such as${D^0} \to {K^ - }{l^ + }\upsilon $, ${D^0} \to {\pi ^ - }{l^ + }\nu $, ${D_s}\to {K^0}{l^ + }\nu $ and ${D_s} \to \eta {l^ + }\nu$, where the form factorsof these decays are discussed. The mass spectra of the charm mesons areobtained. We use a potential quark model and consider the non-relativisticHamiltonian of the charm meson as a bound state of the quark-antiquark system.We take into account the harmonic-type confinement and also Hellmann potential,which is a superposition of the Coulomb and the Yukawa potential. Using thevariational approach along with the harmonic oscillator wave functions, weevaluate the mass spectra of the charm mesons, the form factors and thesemileptonic decay widths of $D_{(s)}$. We present our results for masses of$D, D_s$ and $\eta$, the Isgur-Wise functions, the form factors of thesemileptonic decays, and the branching fractions of the semileptonic decays of$D$ and $D_s$. Our results are motivating.

Investigations of the semileptonic decays of $D$ and $D_s$ into a pseudoscalar meson using the Isgur-Wise Functions