A new class of fractional differential hemivariational inequalitieswith application to an incompressible Navier–Stokes system coupled witha fractional diffusion equation

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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 consistsof a quasilinear evolution equation involving the fractional Caputo derivativeoperator and a coupled generalized parabolic hemivariational inequality.Undercertain general assumptions, existence and regularity of a mild solution tothe dynamical system are established by employing a surjectivity result forweakly–weakly upper semicontinuous multivalued mappings, and a feedbackiterative technique together with a temporally semi-discrete approach throughthe backward Euler difference scheme with quasi-uniform time-steps. Toillustrate the applicability of the abstract results, we consider a nonstationaryand incompressible Navier–Stokes system supplemented by a fractionalreaction–diffusion equation, which is studied as a fractional hemivariationalinequality.

作者简介

Shengda Zeng

Yulin Normal University; Nanjing University

Email: zengshengda@163.com

Stanisław Migórski

Beibu Gulf University; Jagiellonian University

Email: stanislaw.migorski@uj.edu.pl
Doctor of Science, Professor

Weimin Han

University of Iowa

Email: weimin-han@uiowa.edu
Doctor of physico-mathematical sciences, Professor

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