  In this present paper, we introduce and study a dynamical systems involving
fractional derivative operator and nonlocal condition, which is constituted of
a fractional evolution equation and a time-dependent variational inequality,
and is named as fractional partial differential variational inequality (FPDVI,
for short). By employing the estimates involving the one-and two-parameter
Mittag-Leffler functions, fixed-point theory for set-value mappings, and
non-compactness measure theory, we develop a general framework to establish the
existence of smooth solutions to (FPDVI).
