Approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces

In this paper, the approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in a Hilbert space is studied. By using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O’Regan and properties of the α -resolvent operator combined with approximation techniques, we derive a new set of sufficient conditions for the approximate controllability of fractional impulsive evolution system under the assumption that the corresponding linear system is approximately controllable. An example is provided to illustrate the obtained theory.