Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems

In this work, the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems in a Banach space has been established by using the theory of fractional calculus, fixed point technique and also we introduced a new concept called (α,u)(α,u)-resolvent family. As an application that illustrates the abstract results, an example is given.