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Existence of a global attractor for fractional differential hemivariational inequalities

The first author is supported by the Natural Science Foundation of Guangxi Province (2018GXNSFAA281021) and the Foundation of Guilin University of Technology (GUTQDJJ2017062). The second author is supported by the National Natural Science Foundation of China (11471230, 11671282). The third author is supported by the National Natural Science Foundation of China (11772306), Graduates education Teaching Research and Reform Project of China University of Geosciences (YJS2018311), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (CUGGC05)

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  • In this paper, we introduce and study a new class of fractional differential hemivariational inequalities ((FDHVIs), for short) formulated by an initial-value fractional evolution inclusion and a hemivariational inequality in infinite Banach spaces. First, by applying measure of noncompactness, a fixed point theorem of a condensing multivalued map, we obtain the nonemptiness and compactness of the mild solution set for (FDHVIs). Further, we apply the obtained results to establish an existence theorem of the mild solution of a global attractor for the semiflow governed by a fractional differential hemivariational inequality ((FDHVI), for short). Finally, we provide an example to demonstrate the main results.

    Mathematics Subject Classification: Primary: 34D45, 35R11, 35R70; Secondary: 49J53.


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