  Contrary to integer order derivative, the fractional-order derivative of a
non-constant periodic function is not a periodic function with the same period,
as a consequence of this property the time-invariant fractional order system
does not have any non-constant periodic solution unless the lower terminal of
the derivative is plus or minus infinite, which is not practical. This property
limits the applicability areas of fractional derivatives and makes it
unfavorable, for a wide range of periodic real phenomena. Therefore enlarging
the applicability of fractional system to such real area is an important
research topic. In this paper we give a solution for the above problem by
imposing a simple modification on the Gr\"unwald-Letnikov definition of
fractional derivative, this modification consists of fixing the memory length
and varying the lower terminal of the derivative. It is shown that the new
proposed definition of fractional derivative preserves the periodicity.
