On recent developments in the theory of abstract differential equations with fractional derivatives

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) 1], Belmekki and Benchohra (2010) 2], Darwish et al. (2009) 3], Hu et al. (2009) 4], Mophou and N’Guérékata (2009) 6] and 7], Mophou (2010) 8] and 9], Muslim (2009) 10], Pandey et al. (2009) 11], Rashid and El-Qaderi (2009) 12] and Tai and Wang (2009) 13]] 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.