Approximate controllability of a semilinear impulsive fractional stochastic integro-differential inclusions with Poisson jumps

This work explores the approximate controllability of a semilinear impulsive fractional stochastic integro-differential inclusions with Poisson jumps involving the Caputo fractional derivative of order \(q\in (0,1)\). We consider a class of control systems governed by fractional differential inclusions by using Bohnenblust-Karlin's fixed point theorem and stochastic analysis theory to derive a new set of sufficient conditions for the approximate controllability of a semilinear impulsive fractional stochastic integro-differential inclusions with Poisson jumps. Finally, an example is given to illustrate the results obtained.