This paper explores a generalized fractional differential hemivariational inequality, formulated by combining a \(\psi \) -Caputo derivative hemivariational inequality with a \(\psi \) -Caputo fractional differential equation. As a parabolic-type coupled system that integrates fractional derivatives into both variational and differential parts, it can be widely applied to various dynamic situations. To prove the existence of weak solutions, this paper employs a time semi-discretization method, discretizing the time interval and constructing an approximate discrete problem. We utilize the surjectivity result for multivalued pseudomonotone operators to establish the existence of solutions to the discrete problem. Furthermore, we verify the pseudomonotonicity and coercivity of the composite operator and use convergence analysis to ensure the original continuous problem has a solution.
