STOCHASTIC CONTROLLABILITY FOR A NONAUTONOMOUS FRACTIONAL NEUTRAL DIFFERENTIAL EQUATION WITH INFINITE DELAY IN ABSTRACT SPACE

Abstract

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