Approximate Controllability of Impulsive Fractional Partial Neutral Quasilinear Functional Differential Inclusions with Infinite Delay in Hilbert Spaces

In this paper, we consider the controllability problems for a class of impulsive fractional partial neutral quasilinear functional differential inclusions with infinite delay and (α, x)-resolvent family. In particular, a set of sufficient conditions are derived for the approximate controllability of nonlinear impulsive fractional dynamical systems by assuming the associated linear system is approximately controllable. The results are established by using the concept of resolvent family, fractional calculations and fixed point techniques. Finally, an example is provided to illustrate the obtained theory.