ANALYSIS OF A SYSTEM CONSISTING OF A FRACTIONAL HISTORY-DEPENDENT HEMIVARIATIONAL INEQUALITY AND A NONLOCAL DELAY FRACTIONAL DIFFERENTIAL EQUATION

This study presents a new type of system that combines a nonlocal delay fractional differential equation with a fractional history-dependent hemivariational inequality. Using a multivalued operator’s surjectivity, we investigate the existence and uniqueness of the solution to the fractional history-dependent hemivariational inequality. In addition, we highlight the unique solvability of moderate solutions to the problem. In addition, we develop a novel viscoelastic frictional contact issue with internal variables and defer the application of the acquired results in future study.