Existence and regulation analysis for Hilfer–Katugampola fractional neutral hemivariational dynamics with nonlocal initialization and fractional noise

Abstract This paper studies mild solutions and optimal control for Sobolev-type Hilfer–Katugampola fractional neutral stochastic evolution hemivariational inequalities with nonlocal initial conditions, fractional Brownian motion, and Clarke sub-differentials. Using semigroup theory, properties of the Clarke sub-differential, and fixed point methods for multivalued maps, we establish the existence of mild solutions. Furthermore, by employing a restricted Lagrange optimization framework, we derive optimal state–control pairs without assuming uniqueness. A numerical example illustrates the theoretical results.