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Solvability and optimal controls for semilinear fractional evolution hemivariational inequalities
Author(s) -
Lu Liang,
Liu Zhenhai,
Jiang Wei,
Luo Jinlian
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3930
Subject(s) - mathematics , banach space , subderivative , fractional calculus , inequality , fixed point theorem , mathematical analysis , regular polygon , convex optimization , geometry
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.