Geodesic
A~new class of fractional differential hemivariational inequalities
Izvestiya. Mathematics , Tome 87 (2023) no. 2, pp. 326-361

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This paper is devoted to the study of a new and complicated dynamical system, called a fractional differential hemivariational inequality, which consists of a quasilinear evolution equation involving the fractional Caputo derivative operator and a coupled generalized parabolic hemivariational inequality. Under certain general assumptions, existence and regularity of a mild solution to the dynamical system are established by employing a surjectivity result for weakly–weakly upper semicontinuous multivalued mappings, and a feedback iterative technique together with a temporally semi-discrete approach through the backward Euler difference scheme with quasi-uniform time-steps. To illustrate the applicability of the abstract results, we consider a nonstationary and incompressible Navier–Stokes system supplemented by a fractional reaction–diffusion equation, which is studied as a fractional hemivariational inequality.
Keywords: fractional differential hemivariational inequality, Clarke subgradient, $C_0$-semigroup, Navier–Stokes system.
Mots-clés : existence 
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     title = {A~new class of fractional differential hemivariational inequalities},
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S. D. Zeng; S. Migórski; W. Han. A~new class of fractional differential hemivariational inequalities. Izvestiya. Mathematics , Tome 87 (2023) no. 2, pp. 326-361. http://geodesic.mathdoc.fr/item/IM2_2023_87_2_a4/