In this paper, we mainly investigate controlled fractional evolution hemivariational inequalities of degenerate type in Caputo and Riemann-Liouville fractional derivatives of order in respectively. With the help of properties on fractional resolvent operators and generalised Clarke subdifferential, suitable concepts of solutions to addressed systems are formulated and existence results are established. And then, we present the existence of optimal state-control pairs for the limited Lagrange optimal systems governed by fractional evolution hemivariational inequalities of degenerate type. The optimal control results are attained by the compactness of some corresponding fractional resolvent operators.