Solvability of parabolic variational-hemivariational inequalities involving space-fractional Laplacian

The paper is devoted to investigate a new kind of variational-hemivariational inequality of parabolic type driven by a generalized space-fractional Laplace operator, and two multivalued terms which are expressed by the Clarke generalized gradient and convex subgradient, respectively. An existence theorem of weak solutions to the problem is established by applying a surjectivity theorem for the sum of operators combined with results from nonsmooth analysis.