Lipschitz stability of solution sets of Young differential inclusion

We investigate the Lipschitz stability of solution sets to Young differential inclusions driven by families of Hölder continuous functions. The main analytical tool is an appropriate version of Filippov’s Theorem formulated for differential inclusions governed by set-valued Young integrals. Both local and global variants of this theorem are established and subsequently employed to derive Lipschitz-type dependence of solution sets on the right-hand side of the inclusion. The considered framework covers, in particular, differential inclusions driven by fractional Brownian motion. The proofs are based on selection and approximation techniques.