The effects of Clarke sub-differential and Poisson jumps on nonlocal controllability of Sobolev-type fractional stochastic differential inclusions

This paper explores Sobolev-type Atangana–Baleanu fractional stochastic differential inclusions driven by fractional Brownian motion, incorporating Clarke sub-differentials, Poisson jumps, and nonlocal conditions. Through the use of fractional calculus (FC), stochastic analysis (SA), and fixed-point techniques, the authors derive sufficient conditions for nonlocal controllability. The analysis leverages the properties of Clarke sub-differentials and non-smooth analysis. An illustrative example is provided to highlight the practical application and significance of the findings.