Approximate controllability of semilinear nonlocal fractional differential systems via an approximating method

We study the control system governed by a class of abstract nonlocal fractional differential equations. By using the fractional calculus and approximating technique, we give the approximate problem of the control system and get the compactness of approximate solutions set. Then new sufficient conditions for the approximate controllability of the control system are obtained when the compactness conditions or Lipschitz conditions for the nonlocal function are not required.