  The subject of fractional calculus has witnessed rapid development over past
few decades. In particular the area of fractional differential equations has
received considerable attention. Several theoretical results have been obtained
and powerful numerical methods have been developed. In spite of the extensive
numerical simulations that have been carried out in the area of fractional
order dynamical systems, analytical results obtained are very few. In pursuance
to this, present authors have extended local stable manifold theorem in case of
fractional systems \cite{deshpande2016local}. Cong et al. \cite{cong2016stable}
have pointed out discrepancies in the asymptotic expansion of two-parameter
Mittag-Leffler functions with matrix argument (\textit{cf.} Lemma 4 part 2 of
article \cite{deshpande2016local}). In the present communication we give the
corrected expansion of the same and prove the local stable manifold theorem by
following the same approach given in \cite{deshpande2016local}.
