  This paper deals with the controllability for a class of non-autonomous
neutral differential equations of fractional order with infinite delay in an
abstract space. The semi-group theory of bounded linear operators, fractional
calculus, and stochastic analysis techniques have been implemented to achieve
the main result. We prove the existence of mild solution and controllability of
the system by using the theory of measure of non-compactness, fixed point
theorems, and $k$-set contractive mapping. An example is given to demonstrate
the effectiveness of the abstract result.
