In this work, we are concerned with the approximate controllability of fractional nonlinear differential equations with nonlocal conditions of order
in Banach spaces. As far as we know, few articles are investigating this issue. The idea is to see under which sufficient conditions the proposed control problem is approximately controllable. The discussion is based on the theory of resolvent operator, fractional calculus techniques, and Krasnoselskii's fixed point theorem under the assumption that the associated linear system is approximately controllable. The obtained results improve some existing analogous ones on this topic to some extent. Finally, an example is provided to illustrate the applications of the obtained results.