Controllability of fractional neutral stochastic integrodifferential inclusions of order $p \in (0,1]$ p ∈ ( 0 , 1 ] , $q \in (1,2]$ q ∈ ( 1 , 2 ] with fractional Brownian motion

Abstract

This paper investigates the complete and approximate controllability of nonlinear fractional neutral stochastic integrodifferential inclusions of order \(0 < p\leq 1 < q\leq 2\) with fractional Brownian motion (fBm) in finite dimensional space. By using fixed-point theorems, namely the Bohnenblust-Karlin and Covitz-Nadler for the convex and nonconvex cases, a new set of sufficient conditions are formulated which guarantees each type of controllability. The result is established under the assumption that the associated linear stochastic system is completely and approximately controllable. Finally, two examples are presented to illustrate the efficiency of the obtained theoretical results.