Degenerate type fractional evolution hemivariational inequalities and optimal controls via fractional resolvent operators

ABSTRACT

In this paper, we mainly investigate controlled fractional evolution hemivariational inequalities of degenerate type in Caputo and Riemann–Liouville fractional derivatives of order in $(1,2)$ 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.

KEYWORDS:

• Fractional evolution equations of degenerate type
• optimal control
• hemivariational inequalities
• fractional resolvent operator

Acknowledgements

The authors are also thankful to the anonymous referees for their careful reading of the manuscript and for making suggestions which have improved the previous version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by Natural Science Basic Research Program of Shaanxi Province (2017JM1017).