Multivalued Variational Inequalities with Generalized Fractional Φ-Laplacians

In this article, we examine variational inequalities of the form < A(u),v-u >+< F(u),v-u >>= 0,for all v is an element of Ku is an element of K,, where A is a generalized fractional Phi-Laplace operator, K is a closed convex set in a fractional Musielak-Orlicz-Sobolev space, and F is a multivalued integral operator. We consider a functional analytic framework for the above problem, including conditions on the multivalued lower order term F such that the problem can be properly formulated in a fractional Musielak-Orlicz-Sobolev space, and the involved mappings have certain useful monotonicity-continuity properties. Furthermore, we investigate the existence of solutions contingent upon certain coercivity conditions.