  In this paper, a chaos control algorithm for a class of piece-wise continuous
chaotic systems of fractional order, in the Caputo sense, is proposed. With the
aid of Filippov's convex regularization and via differential inclusions, the
underlying discontinuous initial value problem is first recast in terms of a
set-valued problem and hence it is continuously approximated by using Cellina's
Theorem for differential inclusions. For chaos control, an active control
technique is implemented so that the unstable equilibria become stable. As
example, Shimizu--Morioka's system is considered. Numerical simulations are
obtained by means of the Adams-Bashforth-Moulton method for differential
equations of fractional-order.
