A new class of fractional differential hemivariational inequalities
with application to an incompressible Navier–Stokes system coupled with
a fractional diffusion equation
Abstract:
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.