Existence results for abstract fractional differential equations with nonlocal conditions via resolvent operators

In our paper [10] we discussed an error in the recent literature on abstract fractional differential equations and we proposed a different approach to treat these type of problems. By noting that the results by Hernández et al. (2010) [10] are not applicable for problems with nonlocal conditions, in this paper we study the existence of mild solutions for a class of abstract fractional differential equations with nonlocal conditions. An application to the partial differential equation with a fractional temporal derivative and nonlocal conditions is considered.