Approximate controllability of fractional stochastic integro-differential equations with infinite delay of order 1 < α < 2

This paper is mainly concerned with the approximate controllability of fractional stochastic integro-differential equations with infinite delay of order 1 < alpha < 2. Sufficient conditions for approximate controllability of fractional control system are proved under a range condition on the control operator and the corresponding linear fractional control system is approximately controllable. The results are obtained by using the stochastic analysis techniques and fixed point theory. Further, we extend the result to study the approximate controllability of fractional stochastic differential equations driven by Poisson jumps. An example is given to illustrate the theory.