This paper deals with the concept of (integer-order) memristive systems, which are generalized to non-integer order case using fractional calculus. We consider the memory effect of the fractional inductor (fractductor), fractional capacitor and fractional memristor. We also show that the memory effect of such devices can be also used for an analogue implementation of the fractional-order operator, namely fractional-order integral and fractional-order derivatives. This kind of operator is useful for realization of the fractional-order controllers. We present theoretical description of such implementation and we proposed the practical realization and did some simulations and experimental measurements as well.