Qualitative analysis of solution to a new kind of fractional variational inequalities

In this present paper, we first concern the introduction of a new class of evolution systems which are formulated by a fractional evolution equation and a variational inequality. In this sense, we discuss that the problem solution set fractional evolution equation variational inequality (FEEVI, for short) is not empty and the set of all smooth trajectories \(\psi \) $\psi$ of FEEVI is compact in \(C([0,T],\Omega )\) $C([0,T],\mathrm{\Omega })$ through the Gronwall inequality and the Filippov implicit function lemma.