APPROXIMATE CONTROLLABILITY OF IMPULSIVE STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

This paper studies the approximate controllability of an impulsive neutral stochastic integro-differential equation with nonlocal conditions and infinite delay involving the Caputo fractional derivative of order $q\in(1,2)$ in separable Hilbert space. The existence of the mild solution to fractional stochastic system with nonlocal and impulsive conditions is first proved utilizing fixed point theorem, stochastic analysis, fractional calculus and solution operator theory. Then, a new set of sufficient conditions proving approximate controllability of nonlocal semilinear fractional stochastic system involving impulsive effects is derived by assuming the associated linear system is approximately controllable. Illustrating the obtained abstract results, an example is considered at the end of the paper.