semilinear fractional evolution hemivariational inequalities

What is it about?

This paper is concerned with the control systems of semilinear fractional evolution hemivariational inequalities and their optimal controls in Banach space. Firstly, the existence of mild solutions is obtained and proved mainly by using a well-known fixed point theorem of multivalued maps and the properties of generalized Clarke subdifferential. Then, by applying generally mild conditions of cost functionals, we investigate the existence results of the optimal controls for fractional differential evolution hemivariational inequalities. Finally, an example is given to demonstrate the applicability of the main results.

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Why is it important?

To the best of our knowledge, the solvability and optimal controls for fractional evolution hemivariational inequalities are still untreated topics in the literature, and this is one of the motivations of the present work.

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