  Let $(\mathbb{R}_{\alpha ,\beta ,\gamma
}(z))_{m}(z)=z+\sum_{n=1}^{m}A_{n}z^{n+1}$ be the sequence of partial sums of
the normalized Rabotnov functions $\mathbb{R}_{\alpha ,\beta ,\gamma
}(z)=z+\sum_{n=1}^{\infty }A_{n}z^{n+1}$ where $A_{n}=\frac{\beta ^{n}\Gamma
\left( \gamma +\alpha \right) }{\Gamma \left( \left( \gamma +\alpha \right)
(n+1)\right) }.$ The purpose of the present paper is to determine lower bounds
for $\mathfrak{R}\left \{ \frac{\mathbb{R}_{\alpha ,\beta ,\gamma }(z)%
}{(\mathbb{R}_{\alpha ,\beta ,\gamma })_{m}(z)}\right \} ,\mathfrak{R}% \left
\{ \frac{(\mathbb{R}_{\alpha ,\beta ,\gamma })_{m}(z)}{\mathbb{R}% _{\alpha
,\beta ,\gamma }(z)}\right \} ,$
  $\mathfrak{R}\left \{ \frac{\mathbb{R}_{\alpha ,\beta ,\gamma
}(z)}{(\mathbb{% R}_{\alpha ,\beta ,\gamma })_{m}^{\prime }(z)}\right \}
,\mathfrak{R}% \left \{ \frac{(\mathbb{R}_{\alpha ,\beta ,\gamma })_{m}^{\prime
}(z)}{% \mathbb{R}_{\alpha ,\beta ,\gamma }(z)}\right \} .$ Furthermore, we
give lower bounds for $\mathfrak{R}\left \{ \frac{\mathbb{I}\left[ \mathbb{R}%
_{\alpha ,\beta ,\gamma }\right] (z)}{(\mathbb{I}\left[ \mathbb{R}_{\alpha
,\beta ,\gamma }\right] )_{m}(z)}\right \} $ and $\mathfrak{R}\left \{ \frac{%
(\mathbb{I}\left[ \mathbb{R}_{\alpha ,\beta ,\gamma }\right] )_{m}(z)}{%
\mathbb{I}\left[ \mathbb{R}_{\alpha ,\beta ,\gamma }\right] (z)}\right \} $
where $\mathbb{I}\left[ \mathbb{R}_{\alpha ,\beta ,\gamma }\right] $ is the
Alexander transform of $\mathbb{R}_{\alpha ,\beta ,\gamma }$. Several examples
of the main results are also considered.
