Approximate Controllability of Fractional Neutral Stochastic Functional Integro-Differential Inclusions with Infinite Delay

In this paper, we investigate the approximate controllability for a class of fractional neutral stochastic functional integro-differential inclusions involving the Caputo derivative in Hilbert spaces. A new set of sufficient conditions are formulated and proved for the approximate controllability of fractional stochastic integro-differential inclusions under the assumption that the associated linear part of system is approximately controllable. The main techniques rely on the fractional calculus, operator semigroups and Bohnenblust-Karlin's fixed point theorem. An example is given to illustrate the obtained theory.