New insights into solvability of fractional evolutionary inclusions and variational-hemivariational inequalities in contact mechanics

This paper primarily investigates two types of fractional evolutionary systems: one is an evolutionary equation with doubly nonlinear operators, and the other is an evolutionary inclusion with multi-valued upper semicontinuous operators. By utilizing monotone operator theory and the Kakutani-Ky Fan-Glicksberg fixed point theorem, we establish the existence of their solutions under appropriate hypotheses. As practical applications, we first demonstrate the existence of solutions for a special type of fractional variational-hemivariational inequality. Then, two quasi-static viscoelastic contact mechanical models that incorporate fractional Kelvin-Voigt constitutive equations and different frictional contact laws are proposed. The existence of their weak solutions is derived from our abstract mathematical results.