Abstract This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) , Belmekki and Benchohra (2010) , Darwish et al. (2009) , Hu et al. (2009) , Mophou and N’Guérékata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) , Pandey et al. (2009) , Rashid and El-Qaderi (2009)  and Tai and Wang (2009) ] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.