On the approximate controllability for fractional evolution inclusions of Sobolev and Clarke subdifferential type

This article is concerned with the approximate controllability for some fractional evolution inclusions of Sobolev and Clarke subdifferential type, which can be used to study fractional hemivariational inequalities. Using two characteristic solution operators and their fundamental properties via a fixed point theorem for multi-valued maps, we derive sufficient conditions for approximate controllability of linear and semi-linear controlled systems. Finally, two examples are given to illustrate our theory.