Solvability and optimal controls for semilinear fractional evolution hemivariational inequalities |
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| Authors: | Liang Lu Zhenhai Liu Wei Jiang Jinlian Luo |
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| Institution: | 1. College of Science, Nanjing University of Science and Technology, Jiangsu, Nanjing, China;2. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Science, Guangxi University for Nationalities, Guangxi, Nanning, China;3. College of Science, Hezhou University, Guangxi, Hezhou, China |
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| Abstract: | 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. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | solvability optimal control hemivariational inequalities generalized Clarke subdifferential fractional evolution equations subclass 34H05 35R11 49J20 |
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