Approximate controllability of partial fractional neutral stochastic functional integro-differential inclusions with state-dependent delay

Abstract

We study the approximate controllability of partial fractional neutral stochastic functional integro-differential inclusions with state-dependent delay under the assumptions that the corresponding linear system is approximately controllable. Using fractional calculus, stochastic analysis theory, and the fixed-point technique with the properties of analytic \(\alpha \)-resolvent operators, a new set of sufficient conditions for approximate controllability of fractional stochastic functional integro-differential inclusions are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.