On fuzzy fractional differential inclusion driven by variational-hemivariational inequality in Banach spaces

The aim of this paper is to examine an evolution problem (FFDIVHVI) involving a fuzzy fractional differential inclusion and a variational-hemivariational inequality (VHVI) in Banach spaces. First, we show a uniqueness and existence theorem for VHVI under the theory of monotone operators and the surjectivity theorem. Then, by utilizing fixed point theorem for multivalued contraction mapping and fuzzy set theory, we establish the existence result for FFDIVHVI. In addition, it is proven that the collection of all mild trajectories of FFDIVHVI exhibits compactness. Finally, we illustrate the applicability of the abstract theory by a nonlinear quasistatic thermoelastic frictional contact problem for which we provide existence results.